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Paper Citation Record · LEDGER

Logical Aspects of Virtual Double Categories

As of 11 August 2026, this Paper Citation Record lists 100 of 110 outbound references and 0 inbound Pith citation observations for arXiv:2501.17869.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.17869 v2

Coverage vector

measured 100 of 110 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:27:37.587656Z

measured 100 of 100 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

100 of 110 outbound references displayed

  • verified exact8
  • verified fuzzy43
  • unresolved49
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7e75d8df-7c80-48e6-809f-36426417152a · outbound

This paper cites Cartesian Double Categories with an Emphasis on Characterizing Spans.

Logical Aspects of Virtual Double Categories Cartesian Double Categories with an Emphasis on Characterizing Spans

Reference 1

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Observation 1a85d8b3-5f95-46ce-9193-426c19e66b6b · outbound

This paper cites The formal theory of relative monads.

Logical Aspects of Virtual Double Categories The formal theory of relative monads

Reference 2

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Observation 5d6a4b17-add7-457d-8c91-57d6d55dfa67 · outbound

This paper cites The nerve theorem for relative monads.

Logical Aspects of Virtual Double Categories The nerve theorem for relative monads

Reference 3

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Observation 7c9e14c4-07a2-4a1f-b866-14b476f3d02a · outbound

This paper cites Bicategorical type theory: Semantics and syntax.

Logical Aspects of Virtual Double Categories Bicategorical type theory: Semantics and syntax

Reference 4

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source=arxiv_source observed=2026-08-10T20:27:37.124904Z digest=sha256:7f4ee44bef74a767eb8d73024cd04c4ac85b798486402acda62f2e5d37849520

Observation e4e0d78c-bd42-4037-aa92-fb5841b16442 · outbound

This paper cites tangle, 2022.

Logical Aspects of Virtual Double Categories tangle, 2022

Reference 5

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source=arxiv_source observed=2026-08-10T20:27:37.129624Z digest=sha256:102df9f08033f8bfc0d189e1150b5e2ad73c3e7b3193a9ee782e1097b4c9e318

Observation 6fb37720-0d65-45dd-8517-aeb6a69ada20 · outbound

This paper cites Diagrammatic Algebra of First Order Logic.

Logical Aspects of Virtual Double Categories Diagrammatic Algebra of First Order Logic

Reference 6

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Observation 82702859-e07d-46ae-b9ef-3a90fb0a9aec · outbound

This paper cites Exact categories.

Logical Aspects of Virtual Double Categories Exact categories

Reference 7

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Observation 9c22693a-ec4e-484a-af65-0d523134b3a1 · outbound

This paper cites Functorial Semantics for Relational Theories.

Logical Aspects of Virtual Double Categories Functorial Semantics for Relational Theories

Reference 8

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Observation e5615a23-b2e5-4c85-8db0-4c330f1f4a4a · outbound

This paper cites On Doctrines and Cartesian Bicategories.

Logical Aspects of Virtual Double Categories On Doctrines and Cartesian Bicategories

Reference 9

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Observation b50db7bb-1093-4e5f-a146-580c51325a47 · outbound

This paper cites Introduction.

Logical Aspects of Virtual Double Categories Introduction

Reference 10

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Observation fe403f97-1aaf-4fd2-b85d-c2adb559ad95 · outbound

This paper cites T -cat\'egories (cat\'egories dans un triple).

Logical Aspects of Virtual Double Categories T -cat\'egories (cat\'egories dans un triple)

Reference 11

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Observation c2b861dc-4455-43f2-bb5b-d369cd6b29c7 · outbound

This paper cites Generalised algebraic theories and contextual categories.

Logical Aspects of Virtual Double Categories Generalised algebraic theories and contextual categories

Reference 12

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Observation 6c65e9a5-a5e8-46ef-84d5-8589ce4e6ae7 · outbound

This paper cites The Biequivalence of Locally Cartesian Closed Categories and Martin-L \"of Type Theories.

Logical Aspects of Virtual Double Categories The Biequivalence of Locally Cartesian Closed Categories and Martin-L \"of Type Theories

Reference 13

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Observation e3a2ca32-8e3a-419c-80fb-f5c2b3f42757 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 14

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Observation 2a44539c-4e53-4b3a-bb23-1dec4684f5c7 · outbound

This paper cites Bicategories of spans and relations.

Logical Aspects of Virtual Double Categories Bicategories of spans and relations

Reference 15

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Observation 9b8130e4-aef6-4338-a962-b342763d4307 · outbound

This paper cites Carboni, G.

Logical Aspects of Virtual Double Categories Carboni, G

Reference 16

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Observation b61a4cb6-9da1-429b-a09c-b8c9f0eefef9 · outbound

This paper cites Carboni, G.

Logical Aspects of Virtual Double Categories Carboni, G

Reference 17

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Observation 6effc00b-6356-4132-bee3-df8d3d21a5c0 · outbound

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Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 18

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Observation be46a8df-0b0b-479d-baf3-ca85c46ff032 · outbound

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Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 19

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Observation d04e27ee-915e-4f60-b2ec-bde692846de3 · outbound

This paper cites Carboni and R.

Logical Aspects of Virtual Double Categories Carboni and R

Reference 20

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Observation 57756c2d-64a2-409c-b4e4-b00e1fa99daf · outbound

This paper cites Quotients and extensionality in relational doctrines.

Logical Aspects of Virtual Double Categories Quotients and extensionality in relational doctrines

Reference 21

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Observation 7b948e40-4b74-41e7-8223-c2c27f5236b7 · outbound

This paper cites Cauchy-completions and the rule of unique choice in relational doctrines.

Logical Aspects of Virtual Double Categories Cauchy-completions and the rule of unique choice in relational doctrines

Reference 22

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Observation 24d59615-cec4-429c-b711-b1b20fc28835 · outbound

This paper cites The Relational Quotient Completion.

Logical Aspects of Virtual Double Categories The Relational Quotient Completion

Reference 23

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Observation 9bbe261e-3de4-413c-b5ae-a8f8613c30d6 · outbound

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Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 24

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Observation bc898a7c-c6c9-4716-9d83-71ecd25cb602 · outbound

This paper cites Elementary fibrations of enriched groupoids.

Logical Aspects of Virtual Double Categories Elementary fibrations of enriched groupoids

Reference 25

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Observation a370581b-d462-4b63-aea8-1efbeb2b9b7f · outbound

This paper cites A characterisation of elementary fibrations.

Logical Aspects of Virtual Double Categories A characterisation of elementary fibrations

Reference 26

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Observation 50af2d14-ec55-467b-a2ca-8655c6dc4487 · outbound

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Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 27

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Observation 621ccdcf-8235-437c-9c48-4038ff058c45 · outbound

This paper cites Freyd and Andre Scedrov.

Logical Aspects of Virtual Double Categories Freyd and Andre Scedrov

Reference 28

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Observation 203b4389-dc1b-448a-8b1f-6ba6a285d3e1 · outbound

This paper cites Enriched -categories via non-symmetric -operads.

Logical Aspects of Virtual Double Categories Enriched -categories via non-symmetric -operads

Reference 29

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Observation db535124-0f7d-49da-8ba8-7d11882fa0dd · outbound

This paper cites Limits in double categories.

Logical Aspects of Virtual Double Categories Limits in double categories

Reference 30

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Observation 150e924f-79d8-441b-8474-1ebb799d1a67 · outbound

This paper cites Adjoint for double categories.

Logical Aspects of Virtual Double Categories Adjoint for double categories

Reference 31

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Observation de31d887-a5f8-4dfc-94fb-8a68b5f5791d · outbound

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Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 32

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Observation 010373fe-44f9-44a0-988e-45ceb010a9cd · outbound

This paper cites Higher Dimensional Categories -- From Double to Multiple Categories.

Logical Aspects of Virtual Double Categories Higher Dimensional Categories -- From Double to Multiple Categories

Reference 33

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Observation ed4b5d0b-fc66-403d-b858-fc8651c1bae7 · outbound

This paper cites Categories fibrees et descente.

Logical Aspects of Virtual Double Categories Categories fibrees et descente

Reference 34

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Observation c2898040-5cfd-423e-a28e-751fa254d9d6 · outbound

This paper cites Fibrations, Logical Predicates and Indeterminates.

Logical Aspects of Virtual Double Categories Fibrations, Logical Predicates and Indeterminates

Reference 35

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Observation 546a88ef-d126-46ea-b3ff-f0fb4a62a1f1 · outbound

This paper cites On fibred adjunctions and completeness for fibred categories.

Logical Aspects of Virtual Double Categories On fibred adjunctions and completeness for fibred categories

Reference 36

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Observation cf7641e8-4153-47a2-aecc-4bc10838f550 · outbound

This paper cites Some properties of Fib as a fibred 2 -category.

Logical Aspects of Virtual Double Categories Some properties of Fib as a fibred 2 -category

Reference 37

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Observation 843f89f4-9c33-46f8-906b-8cdca0658209 · outbound

This paper cites Representable multicategories.

Logical Aspects of Virtual Double Categories Representable multicategories

Reference 38

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation dc8a8935-ea17-426e-bfaa-59905257f3ae · outbound

This paper cites Factorization systems and fibrations: Toward a fibred birkhoff variety theorem.

Logical Aspects of Virtual Double Categories Factorization systems and fibrations: Toward a fibred birkhoff variety theorem

Reference 39

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 5e077d64-3e63-4d3c-905f-e32e74891d52 · outbound

This paper cites Double categories of relations relative to factorisation systems.

Logical Aspects of Virtual Double Categories Double categories of relations relative to factorisation systems

Reference 40

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local_arxiv, observed 2026-08-10T20:27:37.991937Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.296125Z digest=sha256:d698284177a2add0384c9680d99a6e92a630286acd37c1c81e27c4252f634ea3

Observation cb1f31fb-8892-4645-8038-300aaf29d9e5 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:39.169693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.300755Z digest=sha256:ec70433ee0e815f93f88a95bcd1f16b0ceaa1f743b12861d6c5ad6bfb7b36399

Observation 8972028c-ab74-433c-853b-f1ac30579072 · outbound

This paper cites The groupoid interpretation of type theory.

Logical Aspects of Virtual Double Categories The groupoid interpretation of type theory

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.145775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.305260Z digest=sha256:97e643ca2a44ae307c3a97b8ce2682ade2ebb0502841c67b60728011a8115c62

Observation 0eb8bf2a-dba8-4013-b4a6-04cea79b2731 · outbound

This paper cites Categorical logic and type theory , volume 141 of Studies in Logic and the Foundations of Mathematics.

Logical Aspects of Virtual Double Categories Categorical logic and type theory , volume 141 of Studies in Logic and the Foundations of Mathematics

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.131911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.309175Z digest=sha256:c6e6e9e6dc96fd76cffc157e58fe040bc0676c3ac4b5c9843f490603ad5c84f9

Observation faf0b1ed-3d17-4c2d-8869-093985973729 · outbound

This paper cites Johnstone.

Logical Aspects of Virtual Double Categories Johnstone

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.119500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.313734Z digest=sha256:2684fe59559e9abe820c98fec90daf2021d360fc416b5b36e92286d31bd2e651

Observation 079a2531-b999-4e59-925a-e953939c53a3 · outbound

This paper cites Johnstone.

Logical Aspects of Virtual Double Categories Johnstone

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.106554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.318409Z digest=sha256:621b1a3509594febd7ff3979f442e4f072dba9f8bf36b9cf18db8610d9dd523a

Observation aa38e875-b6d8-4745-93f8-0bf2ef7df3bd · outbound

This paper cites Johnstone and Robert Par\'e, editors.

Logical Aspects of Virtual Double Categories Johnstone and Robert Par\'e, editors

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.091136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.322303Z digest=sha256:2e6cd57053471ee011090c51ad13ac07d023fb2c625e3031648d5edf559dd068

Observation 9fc42f74-cb39-4630-9600-c775e3a1e2eb · outbound

This paper cites Categories of relations and functional relations.

Logical Aspects of Virtual Double Categories Categories of relations and functional relations

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.079761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.326118Z digest=sha256:21b434f579ee396ef264f3d169a7e60134d230894ac69ca8b6455413e6a4f132

Observation ee7454c9-68e3-438c-b602-48a579ac37bb · outbound

This paper cites Relations in categories with pullbacks.

Logical Aspects of Virtual Double Categories Relations in categories with pullbacks

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.068267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.330821Z digest=sha256:f805811c7e0425a69afc27812720005857c8c8e671f2dacdce4b21e1cf5afb28

Observation f47f55d7-206b-4109-bf00-f9cee8e18114 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:39.054120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.334686Z digest=sha256:a5ee6d21dd8c8f52efe3f657d0f695ccc23184495aed9f72bd7ba26117c31440

Observation 5f9628e0-ecd3-41fe-ab6b-320517d6568f · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:39.041325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.338928Z digest=sha256:a010ab1e8e8c279df458df399237ac6d082f8f48ee117e6171217ffcaad6af12

Observation a2df7b73-3e31-4290-872d-2e26f2b93508 · outbound

This paper cites Relations in categories.

Logical Aspects of Virtual Double Categories Relations in categories

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.028421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.343891Z digest=sha256:0d251ff100b2ed67ac4ddabfd143363a09d1a1429854dbf09ee2db3edfa326c8

Observation a88ea5e0-4811-4b44-b95f-00f317b186ff · outbound

This paper cites Augmented virtual double categories.

Logical Aspects of Virtual Double Categories Augmented virtual double categories

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.016561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.348754Z digest=sha256:e7c61fae471fca271ddf390bdf1b12b084a686c98e4aef8835547c9d6666fc63

Observation 40254d60-fba7-4562-94ea-71dd6d2cd161 · outbound

This paper cites Formal category theory in augmented virtual double categories.

Logical Aspects of Virtual Double Categories Formal category theory in augmented virtual double categories

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:39.004551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.353788Z digest=sha256:4e88f55fd5bb43dd7c65c705700b1a9edd80f70d0e724215ca6786b05ff4c0bd

Observation 862e9527-eb98-4605-b27a-1ef803d0317b · outbound

This paper cites Kock and G.

Logical Aspects of Virtual Double Categories Kock and G

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.991359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.358598Z digest=sha256:ff2accb95210fcbdad6dfb79ab98d1a1642b574c666e06fcd9f1cc2fc4b92224

Observation 4e65ee4a-808a-463c-bf50-9db25a649147 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.977750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.364899Z digest=sha256:1771ea318b276a34a27d13358ed4d55928c4625364715e115e6b021a060ddda8

Observation a297ade2-df9e-4b7f-a963-ddf59faaad3c · outbound

This paper cites Double Categories of Relations.

Logical Aspects of Virtual Double Categories Double Categories of Relations

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.958228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.369354Z digest=sha256:436cf732f09558ae329c1962f41764ca92d66908c336caed076a79a97d4aa753

Observation 835a39ef-acec-49a6-b261-74641391f44a · outbound

This paper cites William Lawvere.

Logical Aspects of Virtual Double Categories William Lawvere

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.926891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.373900Z digest=sha256:587dcb669122733a44338a10d711e088f1e49158ebd3f739b6b65dd5b1be8bf3

Observation f0fd1571-d10b-4a40-a77a-fb3b03fb7e8a · outbound

This paper cites William Lawvere.

Logical Aspects of Virtual Double Categories William Lawvere

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.915498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.379920Z digest=sha256:1164cf6a7026ab2d1b61a59c7a9a3e44d28c7eee89d69c0573eb640a0609df9c

Observation 4ad964c9-d801-4c03-ba8d-36500506a49b · outbound

This paper cites William Lawvere.

Logical Aspects of Virtual Double Categories William Lawvere

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.902697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.385387Z digest=sha256:f62af919ae59bc24d26610c114b7b39f06c2fe909498c77652c58bcdef24fbed

Observation 7e3cab4d-d676-426b-9ef8-45015e31ee97 · outbound

This paper cites William Lawvere.

Logical Aspects of Virtual Double Categories William Lawvere

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.884334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.391657Z digest=sha256:6f13e8cf35ae50f6466d759394c67e6778680b9e0bd4437e624da72c7973e82d

Observation 02be3326-dd3a-4393-b02f-d04bda2794ae · outbound

This paper cites Fibrations of predicates and bicategories of relations.

Logical Aspects of Virtual Double Categories Fibrations of predicates and bicategories of relations

Reference 61

Resolution
unresolved
no resolver link, observed 2026-08-10T20:27:37.396427Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:27:37.396427Z digest=sha256:d54218eb61675eb32ee59bb202cd0a5b40657e0c81978d62d742a983e2b09380

Observation aa0dac08-be54-4837-a39c-521b2b47f9cf · outbound

This paper cites Generalized enrichment of categories.

Logical Aspects of Virtual Double Categories Generalized enrichment of categories

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.865234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.401893Z digest=sha256:5ef1243fb404b3c5970fccbe296de160329b05a9d8683042c3c74ad7d44fa273

Observation 8c3162d9-b77a-4f3c-ad29-746615910a11 · outbound

This paper cites Higher Operads, Higher Categories , volume 298 of London Mathematical Society Lecture Note Series.

Logical Aspects of Virtual Double Categories Higher Operads, Higher Categories , volume 298 of London Mathematical Society Lecture Note Series

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.854090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.406650Z digest=sha256:7f72811b3356aff66ba4b524ef486f0c5932af8bb1cfbbed78aff9eb44e81eef

Observation 925898ac-8443-4a84-be29-ab9457099510 · outbound

This paper cites Licata and Robert Harper.

Logical Aspects of Virtual Double Categories Licata and Robert Harper

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.841657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.412296Z digest=sha256:1cd08074b27aef2582df902a02f267bbf33ab556f1a8e5ca00edc6289afe3e02

Observation 5f3a9273-b372-4769-9a0c-50f34116bc64 · outbound

This paper cites FORMAL CATEGORY THEORY.

Logical Aspects of Virtual Double Categories FORMAL CATEGORY THEORY

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.827729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.417274Z digest=sha256:8a9b03386e0a242b4d8c0ff863d5479991817049252e2f2332b665c294478405

Observation 43c8bf2a-5aa6-4927-aaa7-145d54f55bd1 · outbound

This paper cites Laretto, F.

Logical Aspects of Virtual Double Categories Laretto, F

Reference 66

Resolution
unresolved
no resolver link, observed 2026-08-10T20:27:37.422395Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:27:37.422395Z digest=sha256:8d9bd2074db11038fafb568c7f14a663b02558fc1c118575c6b80e86d5bb0c64

Observation 046cc836-f6f0-4d48-b71d-4272ec7ac8bc · outbound

This paper cites ( Co )End Calculus , volume 468 of London Mathematical Society Lecture Note Series.

Logical Aspects of Virtual Double Categories ( Co )End Calculus , volume 468 of London Mathematical Society Lecture Note Series

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.806261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.427952Z digest=sha256:f520aa83ede2e38df796347fbc0d3d180a9d2f4b20df4d22db1ae6a1e3dda01a

Observation 24c9518c-dd6d-4e9f-a9c6-ba1517891dc2 · outbound

This paper cites Categorical notions of fibration.

Logical Aspects of Virtual Double Categories Categorical notions of fibration

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.793022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.433071Z digest=sha256:16a4ae99fd964d804fda4c94cb49f6158175e24ff92289853206f637f4945aff

Observation 3b12e345-43fe-4734-962c-a2143223a4e8 · outbound

This paper cites Lambek and P.

Logical Aspects of Virtual Double Categories Lambek and P

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.776515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.439825Z digest=sha256:3f2e17e80c67350cb63070855935f3b1384ce62e242d0b44e56d2ca459bea997

Observation 1a572ee3-15c7-4884-9e36-56fb0deb3ac4 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 70

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.762901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.445348Z digest=sha256:0479b6f4b94f91a88602c96ee4eb3f7279645a605a01bdf5cb839071a01ea021

Observation 30c81902-113a-4408-bf4a-4a6c13f20734 · outbound

This paper cites Exact completions and toposes.

Logical Aspects of Virtual Double Categories Exact completions and toposes

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.748121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.449601Z digest=sha256:1a2fb4a50306f7dc114f009c103b91615e01da54940efb50fb4ba88c5f926e9c

Observation eaea0d88-516c-415b-8ba2-18a20c12d212 · outbound

This paper cites Relations in categories, 2000.

Logical Aspects of Virtual Double Categories Relations in categories, 2000

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.734762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.454530Z digest=sha256:c7e26212df54ca92304d43fbf9f915ef19e4e631d63fa067a47920d838230100

Observation f6552ce5-9484-4fcc-bdcf-42324d78caec · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 73

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.720743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.459007Z digest=sha256:77fe360d7a784dbe18f1027c03e674350fae1a54e7aebf6a24ad496d313cb644

Observation 2e0bc492-e6eb-47ae-92b4-e1c320a059ab · outbound

This paper cites Triposes, exact completions, and H ilbert's -operator.

Logical Aspects of Virtual Double Categories Triposes, exact completions, and H ilbert's -operator

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.706949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.463616Z digest=sha256:8f2849ecd4f0f795db96f0e7b08dbae4954537c1ee515b8e08b65ff9d6c02b75

Observation 65c79f02-1b0b-400b-8e29-954a0766d72f · outbound

This paper cites Elementary quotient completion.

Logical Aspects of Virtual Double Categories Elementary quotient completion

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.690345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.468657Z digest=sha256:9ad2fe85bb3cbc2ed6ed3cdf7ea8fd0b86c090247a424fb54ee7f2866d5474fb

Observation 2a770bd6-2bdd-43d7-8593-436c57707829 · outbound

This paper cites Quotient completion for the foundation of constructive mathematics.

Logical Aspects of Virtual Double Categories Quotient completion for the foundation of constructive mathematics

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.676859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.473232Z digest=sha256:8a5352ccceba813c7d589263a0bdc039e935f1b044cb40c89827a8ec2edc80c2

Observation 21d230b3-32aa-4d33-9452-e98c0055a370 · outbound

This paper cites Comprehension and quotient structures in the language of 2-categories.

Logical Aspects of Virtual Double Categories Comprehension and quotient structures in the language of 2-categories

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.662755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.478866Z digest=sha256:d6dbdcadacfb8f8bd9391407310429cee7934ffbcd615796fe01c659c9f8374e

Observation 0ad39747-5066-4fec-ae4f-2562d3257c5c · outbound

This paper cites String Diagrams For Double Categories and Equipments.

Logical Aspects of Virtual Double Categories String Diagrams For Double Categories and Equipments

Reference 78

Resolution
unresolved
no resolver link, observed 2026-08-10T20:27:37.483722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:27:37.483722Z digest=sha256:396f71b246f5cab989a993da451f73716a0f92a9b13b145970e09070ffd14616

Observation c380ce5e-9d96-4a48-8144-45945667cf39 · outbound

This paper cites An Internal Logic of Virtual Double Categories.

Logical Aspects of Virtual Double Categories An Internal Logic of Virtual Double Categories

Reference 79

Resolution
verified exact
local_arxiv, observed 2026-08-10T20:27:37.872533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.489063Z digest=sha256:a62f6be49147ee2f59f2cbd6ab09cf2e8b1ca91dd10bf3f47f303b8c8368a99d

Observation 7920a0db-38df-467e-9fdb-5a06e42b1c2c · outbound

This paper cites New and Daniel R.

Logical Aspects of Virtual Double Categories New and Daniel R

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.650219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.493627Z digest=sha256:859477095ec9577c98856b681a676af62a31a07f86da18202b48931fe879c4c4

Observation a1d75bc1-b600-4b16-9601-382a799bdd07 · outbound

This paper cites Towards a directed homotopy type theory.

Logical Aspects of Virtual Double Categories Towards a directed homotopy type theory

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.637679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.499311Z digest=sha256:ba622ec2ba6fb8826134cdeebd5c94a5921c524cd98711e6f0e2dc9a41e248d6

Observation a3d3c00e-282c-438a-a3cc-2854bb925265 · outbound

This paper cites First order theories as double lawvere theories.

Logical Aspects of Virtual Double Categories First order theories as double lawvere theories

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.623524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.503717Z digest=sha256:6ed4437b1d1f58e2dec5f0603ff40260da6880dbc64307f609b8c80820c071ef

Observation 2d07d979-dc91-4214-8a7e-94315678428d · outbound

This paper cites Morphisms of rings.

Logical Aspects of Virtual Double Categories Morphisms of rings

Reference 83

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.610322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.509865Z digest=sha256:7c66078afc192fb9c4371d52adf6bbe1014db4e9489f2b53bf99287d3a3aa48d

Observation ad4c9217-649b-46da-9d4a-30bab917b30c · outbound

This paper cites Products in double categories, revisited, 2024.

Logical Aspects of Virtual Double Categories Products in double categories, revisited, 2024

Reference 84

Resolution
unresolved
no resolver link, observed 2026-08-10T20:27:37.513989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:27:37.513989Z digest=sha256:4ccea9bcfc2ad8f9276708e2abd3b22d9303ff3ec8638da0ebafc2a346e1d85a

Observation acbb53c4-24cc-41cc-86f8-c3b762509368 · outbound

This paper cites Transposing cartesian and other structure in double categories.

Logical Aspects of Virtual Double Categories Transposing cartesian and other structure in double categories

Reference 85

Resolution
verified exact
local_arxiv, observed 2026-08-10T20:27:37.784398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.518809Z digest=sha256:8d16c672e4096f8ecddbdc45989412a8a8845a0e095bd12bcd6041bbbbd4157d

Observation 16bf1c1d-7125-45d2-b5b9-4295da7486b9 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 86

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.597452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.523064Z digest=sha256:7cca2687e8d935cabd7370eae2966d015b1ddc853a7b15de4f9762b86a1d1681

Observation e09232ae-d0e2-4f5f-bba3-754f6b1f4616 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 87

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.581624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.527046Z digest=sha256:f46f616d64abacedf021f3676033bf4b91bf14153689afd1b8fdb820e65ed40b

Observation 7d422763-a10f-40d2-9ba2-285d90dfcda3 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 88

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.566723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.530931Z digest=sha256:fe13aa1c3e4016564fa554068c6fc30bc49abae0a8b3c3cf8be898b8087f8a31

Observation cdffad47-5f32-4c66-b6a8-493d45dd7e52 · outbound

This paper cites Palmgren and S.

Logical Aspects of Virtual Double Categories Palmgren and S

Reference 89

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.553648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.534441Z digest=sha256:a253b7ec1097cd785047720f72fb0f739229bdefd48d77114b3e675523604fb5

Observation 5518d301-af1a-4520-aa94-84acea21de6f · outbound

This paper cites Formal category theory in -equipments i, 2024.

Logical Aspects of Virtual Double Categories Formal category theory in -equipments i, 2024

Reference 90

Resolution
verified exact
raw_fallback, observed 2026-08-10T20:27:37.763145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.538947Z digest=sha256:28dea4cf194371bf1d4af7b20fb3c5d02cfdc4346a0f0a52ab5dff01f73a277b

Observation 24c7d2cf-da56-4066-af02-e789ab300e77 · outbound

This paper cites Kan extensions and the calculus of modules for --categories.

Logical Aspects of Virtual Double Categories Kan extensions and the calculus of modules for --categories

Reference 91

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.539069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.544319Z digest=sha256:7b98df6624707e0f32eae30f36b7dbd9167668ea44e1894608214ea937a20307

Observation 399af00e-9b5b-4478-9bbf-2d2f6bdc0951 · outbound

This paper cites Elements of - Category Theory.

Logical Aspects of Virtual Double Categories Elements of - Category Theory

Reference 92

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.524097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.548977Z digest=sha256:69b60b62c7ed11b03693dc56283c4e353153a9154b2518f081dbff07d39ddc3a

Observation df555adc-a239-48b7-9f56-d224ff1aa78e · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 93

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.508350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.553696Z digest=sha256:bf92c6b6f1a32a4bf6957f5a83a1b2991eaf2e1bc691fef360353266349f99ee

Observation 5f2baeaf-3bc6-4e98-a65a-cbc9f7d37f10 · outbound

This paper cites an unresolved cited work.

Logical Aspects of Virtual Double Categories Unresolved cited work

Reference 94

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:27:38.492583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.558441Z digest=sha256:a8a03fa35adeb5a9e06cf9fefafed6ec1fe74ebed8899a45c5ca62fb0ddd6191

Observation 8e5b7773-e6d0-467d-83d1-8849ec957b47 · outbound

This paper cites Selinger.

Logical Aspects of Virtual Double Categories Selinger

Reference 95

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.479501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.562963Z digest=sha256:30a8cdf6347c2afb316dc58b83e681d1d14d9a6e52160b399310dedd5d459265

Observation 773cf4df-87c6-4e58-8263-3f287dcd26be · outbound

This paper cites Framed bicategories and monoidal fibrations.

Logical Aspects of Virtual Double Categories Framed bicategories and monoidal fibrations

Reference 96

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.454645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.567286Z digest=sha256:513dcfa6aeddfb059fe18ec2b952d98a86e899f9591766477fa6d606ad4d0571

Observation 83526935-bf01-4449-9ea3-b6b0889449d7 · outbound

This paper cites Compact closed bicategories.

Logical Aspects of Virtual Double Categories Compact closed bicategories

Reference 97

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.434750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.572275Z digest=sha256:053c549f3a5cf63afd7ee66f92fad0ad19092c48101413730142176c224b26f0

Observation e9754022-f6db-4619-a565-8f0f8ffb8c60 · outbound

This paper cites Streicher.

Logical Aspects of Virtual Double Categories Streicher

Reference 98

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.409011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.577102Z digest=sha256:0d28cdafe7d7f7431f88953e08cad57e63a1d587f8aeb4d6486ac5fecb6809d1

Observation 241fab14-f8ed-4eb9-a07d-0448804282fe · outbound

This paper cites Fibered Categories a la Jean Benabou.

Logical Aspects of Virtual Double Categories Fibered Categories a la Jean Benabou

Reference 99

Resolution
unresolved
no resolver link, observed 2026-08-10T20:27:37.582868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:27:37.582868Z digest=sha256:cf0f428922344f826389508d7bfd55d917cbac98a9901f42c731d79565fe2807

Observation 5ab73f6c-c9ca-4a00-b7b4-78d43264c295 · outbound

This paper cites La teoria delle relazioni nello studio di categorie regolari e di categorie esatte.

Logical Aspects of Virtual Double Categories La teoria delle relazioni nello studio di categorie regolari e di categorie esatte

Reference 100

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:27:38.365607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=arxiv_source observed=2026-08-10T20:27:37.587656Z digest=sha256:96c4d650432f9a4ca950db92f40e04042c1ea1513fee4bb33816679bb0dbf45e

Pith citing papers

No inbound Pith citation observations are available.