Paper Citation Record · LEDGER

Ultracategories via Kan extensions of relative monads

As of 19 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2506.09788.

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

pith.paper-citation-record.v1
2506.09788 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:48:35.910652Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

40 of 40 outbound references displayed

verified exact1
verified fuzzy18
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 29bfd262-37e8-48be-a84b-59e834827cd1 · outbound

This paper cites Altenkirch, J.

Ultracategories via Kan extensions of relative monads Altenkirch, J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:43.892582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 71000dd8-8645-42df-b964-b2b46e653bb3 · outbound

This paper cites Altenkirch, J.

Ultracategories via Kan extensions of relative monads Altenkirch, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:43.727622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d041109d-78ec-4453-b938-32c7042f71e1 · outbound

This paper cites Arkor and D.

Ultracategories via Kan extensions of relative monads Arkor and D

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:43.520021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1b84b831-0254-4df5-b593-2e0c00ede7af · outbound

This paper cites Adámek and L.

Ultracategories via Kan extensions of relative monads Adámek and L

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:43.368028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b656e04f-363c-4465-9196-8ceb40fd98fc · outbound

This paper cites Bicategories of algebras for relative pseudomonads.

Ultracategories via Kan extensions of relative monads Bicategories of algebras for relative pseudomonads

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T04:48:31.644243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70e21e3a-d280-4124-a058-5ab3ab56b7ab · outbound

This paper cites Towards a General Theory of Dependent Sums.

Ultracategories via Kan extensions of relative monads Towards a General Theory of Dependent Sums

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:48:36.175858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d833f217-6433-4a00-8559-a4d0a3c917da · outbound

This paper cites Bozapalides.

Ultracategories via Kan extensions of relative monads Bozapalides

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:43.127222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e9941e7e-c306-42a9-a171-1ccfcc43f428 · outbound

This paper cites Bozapalides.

Ultracategories via Kan extensions of relative monads Bozapalides

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:42.896342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e86279e0-09cd-40a9-a474-fa2d5d7389a8 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:42.693992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9fef340c-2b49-4b8f-846f-0050897a1f9f · outbound

This paper cites The geometry of Coherent topoi and Ultrastructures.

Ultracategories via Kan extensions of relative monads The geometry of Coherent topoi and Ultrastructures

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T04:48:32.151057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddd792ed-0c27-40ce-8e65-23f8b53f7f4d · outbound

This paper cites Eilenberg and J.

Ultracategories via Kan extensions of relative monads Eilenberg and J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:42.501356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 34a064d4-33ca-467e-8591-5f92b0994962 · outbound

This paper cites Fiore, N.

Ultracategories via Kan extensions of relative monads Fiore, N

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:42.364066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 20507f9f-5433-4243-b28c-0d13ba0d082f · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:42.147372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1aace39b-15cb-48b0-9661-107586733b11 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:41.919953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation acda3bde-09d1-4e92-a44c-8876fc2fbd97 · outbound

This paper cites Ultracategories as colax algebras for a pseudo-monad on CAT.

Ultracategories via Kan extensions of relative monads Ultracategories as colax algebras for a pseudo-monad on CAT

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T04:48:32.800046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64867882-272a-4104-90e9-18918ac54349 · outbound

This paper cites Notes on Lax Ends.

Ultracategories via Kan extensions of relative monads Notes on Lax Ends

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T04:48:32.888569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98d9cefe-b1b6-459c-a87c-7ec7a74973c8 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:41.698816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 527b36dd-8b72-46f2-a53e-ca7b2f66fa66 · outbound

This paper cites Johnson and D.

Ultracategories via Kan extensions of relative monads Johnson and D

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:41.569165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7357c674-b6cf-4827-acf6-938dca39f4a7 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:41.310699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9fe684fe-a5c9-4b92-a796-18e6c1fea63e · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:41.111595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8afbf0cb-1880-4619-a01f-d5190765b903 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:40.929657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ceeffaf1-f1c6-4a89-b981-6cc2103e6b1c · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:40.717741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1601473e-9f67-4670-bc68-2ac813095880 · outbound

This paper cites Leinster.

Ultracategories via Kan extensions of relative monads Leinster

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:40.546029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation be2274f0-e7a9-496b-9ff1-a61f56d065e8 · outbound

This paper cites Leinster.

Ultracategories via Kan extensions of relative monads Leinster

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:40.307388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5cac41c8-ca80-4cb2-ab8a-da123f847e27 · outbound

This paper cites Loregian.

Ultracategories via Kan extensions of relative monads Loregian

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:40.136673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4edf707b-f062-4c22-beda-7a64c72cda12 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:39.885613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 83c1aa25-0cf0-4bd7-b4ff-f8dbdadd54bf · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:39.665489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cc8bf53f-af8f-4b56-9ee5-daf1a90c1ce1 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:39.377477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c21987e-68d3-41ae-8043-c9804758a629 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:39.143452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4cadd08d-d61e-405e-8caf-342d465260c1 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:38.868081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 080a3564-e5bc-48f5-a6b4-798b5ecb9749 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:38.597705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d77cf3a-d258-4830-b6ab-8afd9610371d · outbound

This paper cites Marmolejo.

Ultracategories via Kan extensions of relative monads Marmolejo

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:38.402202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 53222e58-89ba-40d1-b400-ec81547dced1 · outbound

This paper cites Marmolejo and R.

Ultracategories via Kan extensions of relative monads Marmolejo and R

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:38.168894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bffa4b4b-19c6-4c82-8206-adb9165dbee6 · outbound

This paper cites Marmolejo and R.

Ultracategories via Kan extensions of relative monads Marmolejo and R

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:37.950217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2412c301-9632-449c-ac37-9651d258ae06 · outbound

This paper cites Moraschini, J.

Ultracategories via Kan extensions of relative monads Moraschini, J

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:37.714544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 365e7b8c-d7b3-47ef-acfe-cca29e35021b · outbound

This paper cites Rosolini.

Ultracategories via Kan extensions of relative monads Rosolini

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:37.441118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a82cb1f8-1e7b-4e85-91f6-f0047be6c945 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:37.160357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9eeb82aa-96d3-4a05-83e1-f3eba11615c7 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:36.950685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e75454e8-34f8-45d7-b10c-8b6900d6acbb · outbound

This paper cites Szlachányi.

Ultracategories via Kan extensions of relative monads Szlachányi

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:48:36.693947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8600d975-3b70-4815-bc7a-df3dac546df0 · outbound

This paper cites an unresolved cited work.

Ultracategories via Kan extensions of relative monads Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:48:36.416786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.