Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-08T22:46:26.028193Z
Paper Citation Record · LEDGER
As of 9 August 2026, this Paper Citation Record lists 100 of 108 outbound references and 1 inbound Pith citation observation for arXiv:2502.04440.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-08T22:46:26.028193Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-08T22:46:25.676892Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-08T22:46:26.890034Z
100 of 108 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation d8e243fb-dead-46b9-8532-f07803f07f20 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ea11b1d-2c1e-42f5-9358-7a245b845c80 · outbound
Unitary Categorical Symmetries Unitary Categorical Symmetries
Reference 2
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 176e8279-63d9-4965-8b28-f2882c2b0850 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 53720b4a-2a53-41a8-9d6d-67409bdf4d0c · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 4
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Unavailable: canonical work link unavailable.
Observation d1c1e377-8f0a-42cd-bc8f-ca09ac7bd805 · outbound
Unitary Categorical Symmetries A convenient tool to characterise and classify irreducible ∗-representations of the tube algebra is the so-called sandwich construction [10–12]
Reference 5
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Observation b2a3eb78-ce64-4cc1-a98f-497221b42a9f · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 6
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Observation 9039021a-2b20-489b-964c-1ae71f3b4a3e · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 7
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Observation c40a3c53-eb07-44ee-accd-26b42fa09d88 · outbound
Unitary Categorical Symmetries Tube algebras, excitations statistics and compactification in gauge models of topological phases
Reference 8
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Unavailable: canonical work link unavailable.
Observation c584bf42-3a97-49b2-908c-2242e2274605 · outbound
Unitary Categorical Symmetries Using this, the unit of Tube(C) can be written as 3 = X [µ] ∈ πD−2(C) 1µ µ Idµ , (6) where 1 ∈ Cdenotes the monoidal unit in C
Reference 9
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Unavailable: canonical work link unavailable.
Observation c4e61610-c27e-4807-8f17-a21eb4e118c5 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 10
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Observation c64263a5-80bc-4cb7-905c-c7c5add52825 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 11
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Observation 75d6545b-df9a-4757-9f1e-35f52ae5b8da · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 12
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Observation b28710da-9575-49c7-a5cf-c1e98fad940f · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 13
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Observation af963f86-4acc-490d-81bb-13e52275cc8d · outbound
Unitary Categorical Symmetries The assign- ment A 7→ A∨ then extends to an op-monoidal func- tor12 ∨ : C → Cop
Reference 14
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Unavailable: canonical work link unavailable.
Observation 223d745f-a721-455d-9e97-60b8668c7d4a · outbound
Unitary Categorical Symmetries We assume this †-structure to be compat- ible with the monoidal structure on C in the sense that ⊗ : C × C → Cis a †-functor13 with unitary coherence data 14
Reference 15
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Observation ad716985-2cc6-451e-a6cd-533b6004c646 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 16
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Observation fcbdc7a7-b9ef-4ff9-b0e3-54309b655aa7 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 17
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Observation 4b2ba797-9615-4f97-b5b7-8a6c070be741 · outbound
Unitary Categorical Symmetries The associated irreducible representation R = R(x,ρ) of 15 Here, we use the notation gx := gxg−1 for the conjugation action of a group element g ∈ G on a group element x ∈ G
Reference 18
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Observation f56f1479-c28c-4472-afe4-2a8e982c724f · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 19
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Observation b89eb7d1-a446-4b6c-9e9c-82449805cee4 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 20
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Observation 1506ff3b-db0e-4c9f-922f-a90a7a6e7ed4 · outbound
Unitary Categorical Symmetries symmetric bicharacter χ : A × A → U (1),
Reference 21
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Unavailable: canonical work link unavailable.
Observation be9ea36f-47ad-4bbe-bca0-a8edebbe1115 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 22
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Observation f01770ac-691a-4c36-b5d2-90c127f4fc71 · outbound
Unitary Categorical Symmetries (75) The pentagon equation then admits the following solu- tion for the associator [52], (76) where the self-inverse (2 ×2)-matrix A is given by A = Ç −a 1/λ −aλ a å
Reference 23
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Unavailable: canonical work link unavailable.
Observation dd7f012a-a568-457d-9ef7-8bf93668f4b3 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 24
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Observation 41e83f82-921c-4537-ba75-6524836f7d22 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 25
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Unavailable: canonical work link unavailable.
Observation 8683c8f0-e72f-4b6e-bd24-f63d7b92f3fa · outbound
Unitary Categorical Symmetries In this case, the associ- ated tube algebra is simply the group algebra C[G] of G with ∗-structure given by inversion [9]
Reference 26
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Observation 8beb4bfc-329e-4194-b61d-282a7308d22e · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 27
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Observation e3cdf8cd-1f29-47dc-9c75-e5352330d86e · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 28
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Observation ec75b0d1-55f0-491d-bef4-b1faafc3a0d8 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 29
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Observation 65a574a7-f5e0-442a-a266-5f2237ca8992 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 30
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Observation d26667e8-6c56-47b2-88b2-c840697634ed · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 31
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 51f7333f-dd1c-4ff6-8be5-6ff3c2c1b390 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 32
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 33de9f0d-7b16-47f9-a587-9ce4090382fb · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 33
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 3576a6f9-b03b-4e3a-a880-2d9513dc51f5 · outbound
Unitary Categorical Symmetries The corresponding irreducible representation bρ of “G is then given by bρ = Ind “G “Ga (a ⊗ ρ) , (141) 15 where we defined “Ga := A∨ ⋊λ Ga
Reference 34
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation e5d2ee3b-2efa-442c-99b7-b8621d777325 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 35
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Observation 00cb3bc4-18b7-4132-bc6e-22505e27b950 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 36
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Observation 8227ff0a-b609-4f33-abaf-d6f9daef0c9c · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 37
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Observation 73e40875-5b4b-4f1e-8825-b6f1f0463449 · outbound
Reference 38
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Observation a2c6beda-037d-44c4-a863-ee0fce86019b · outbound
Unitary Categorical Symmetries Generalized Global Symmetries
Reference 39
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Observation c000c92c-d434-4c17-abcd-74720238dcf3 · outbound
Unitary Categorical Symmetries Non-Invertible Higher-Categorical Symmetries
Reference 40
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Observation 453fd02a-a13c-4226-b031-f7abed66017e · outbound
Unitary Categorical Symmetries What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
Reference 41
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Observation d9c21083-4101-4a13-8bb6-83c32a00f87d · outbound
Unitary Categorical Symmetries ICTP Lectures on (Non-)Invertible Generalized Symmetries
Reference 42
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Unavailable: canonical work link unavailable.
Observation 65f21f51-1bff-4597-a25a-4246a2391fb5 · outbound
Unitary Categorical Symmetries Ocneanu, Chirality for operator algebras , World Sci
Reference 43
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 82cc3e19-f6df-4726-8e7b-f5cc88a063a7 · outbound
Unitary Categorical Symmetries Representation theory for categorical symmetries
Reference 44
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Observation e8ef5c7c-a3dc-4330-b273-1b76f8fe30e5 · outbound
Reference 45
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Unavailable: canonical work link unavailable.
Observation 83fcfda0-a6f2-4d17-8064-f45202939564 · outbound
Unitary Categorical Symmetries Symmetry TFTs from String Theory
Reference 46
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Observation 2c21c0ed-932f-4eee-a06f-e31833f4981e · outbound
Unitary Categorical Symmetries Topological symmetry in quantum field theory
Reference 47
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Unavailable: canonical work link unavailable.
Observation 1695c051-fad4-4c00-993f-24abe533e0a1 · outbound
Unitary Categorical Symmetries Higher S-matrices
Reference 48
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d59b2780-a5fe-4642-b5a8-84051edfd0db · outbound
Unitary Categorical Symmetries Higher S-matrices and higher modular categories
Reference 49
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6dcc1423-6f5c-493d-96f7-8746ff0ac654 · outbound
Unitary Categorical Symmetries Johnson-Freyd and D
Reference 50
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Observation e528bf00-8078-4ce2-ad00-cf327c455843 · outbound
Unitary Categorical Symmetries Neshveyev and M
Reference 51
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation eb049a87-6fb1-474c-88e2-57542c105d54 · outbound
Unitary Categorical Symmetries Izumi, The structure of sectors associated with Longo-Rehren inclusions
Reference 52
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 9bdfaa01-d953-4b1e-8532-3f4837a9f468 · outbound
Unitary Categorical Symmetries Asymptotic density of states in 2d CFTs with non-invertible symmetries
Reference 53
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Unavailable: canonical work link unavailable.
Observation 4b178296-d60e-437f-853c-3eea38e69afd · outbound
Unitary Categorical Symmetries Osterwalder and R
Reference 54
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d7f0c6a5-7872-45e1-8046-00b7dcc00f53 · outbound
Unitary Categorical Symmetries Osterwalder and R
Reference 55
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Observation d3148781-f9bc-46ef-89d4-f877aefd8e5b · outbound
Unitary Categorical Symmetries Reflection Positivity Then and Now
Reference 56
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Observation 66298871-4b96-4c74-84a0-e924dda0ed07 · outbound
Unitary Categorical Symmetries Reflection positivity and invertible topological phases
Reference 57
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Observation cd915055-2780-48de-9de6-59ba707b87b5 · outbound
Unitary Categorical Symmetries Ferrer, B
Reference 58
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Unavailable: canonical work link unavailable.
Observation 57db8056-330d-4278-99a8-f79e44a53ea0 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 59
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2328f528-b7a7-4479-9b38-6536d4e7db34 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 60
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ac84e5ec-f2ed-4620-b533-43e8eed28a8b · outbound
Unitary Categorical Symmetries Invariants of Piecewise-Linear 3-Manifolds
Reference 61
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Observation 13ec4c33-1bfd-4a9b-aee2-073bcb6ed37d · outbound
Reference 62
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 9f6db2e9-ef9b-48c2-9d71-9903d722c122 · outbound
Unitary Categorical Symmetries Fusion 2-categories and a state-sum invariant for 4-manifolds
Reference 63
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Unavailable: canonical work link unavailable.
Observation 65e629dc-73be-4f14-9db1-b8701ff6dcfe · outbound
Unitary Categorical Symmetries Galindo, On braided and ribbon unitary fusion categories, Canadian Mathematical Bulletin 57 (2014), no
Reference 64
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 058ffe8d-883a-4a96-b895-d88c93b8c6f0 · outbound
Unitary Categorical Symmetries Etingof, S
Reference 65
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Observation bc676ec5-7994-4e75-b22c-8b7160833810 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 66
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1cf1580c-fdf9-4dd7-8e6a-f932918fdc83 · outbound
Unitary Categorical Symmetries Sunder and N
Reference 67
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 35449d39-80b7-43be-a426-baac293e3775 · outbound
Unitary Categorical Symmetries On a class of selection rules without group actions in field theory and string theory
Reference 68
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Unavailable: canonical work link unavailable.
Observation edac4131-55bf-42f7-baea-24d3da9273b2 · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 69
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 90f83d37-b261-43a8-b3f5-54b128697555 · outbound
Unitary Categorical Symmetries Gruen and S
Reference 70
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Observation e0049832-b1cb-4969-8868-4b2c98951be1 · outbound
Unitary Categorical Symmetries Hardiman and A
Reference 71
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Observation 1adb1b16-3370-4ca2-b84e-293ce5d423c7 · outbound
Unitary Categorical Symmetries Higher-Dimensional Algebra V: 2-Groups
Reference 72
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Unavailable: canonical work link unavailable.
Observation 60f8d681-abcb-4b0a-985b-5066f7bb0aa6 · outbound
Unitary Categorical Symmetries On 2-Group Global Symmetries and Their Anomalies
Reference 73
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Observation 3fdfdca6-1e90-44cc-b235-e27cb88a297f · outbound
Unitary Categorical Symmetries Bakalov and A
Reference 74
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Observation 51cfdd77-14d2-4262-915a-8d8c7108126f · outbound
Unitary Categorical Symmetries Unitary fusion categories
Reference 75
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Observation 8f0ab8c2-b807-4769-a4f0-348126d17a47 · outbound
Unitary Categorical Symmetries Penneys, Unitary dual functors for unitary multitensor categories, Higher Structures (2018)
Reference 76
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Observation d6d56a0c-dd0f-4790-9c3c-b967009d964d · outbound
Unitary Categorical Symmetries Bhowmick, S
Reference 77
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Observation d2abb5c8-4391-4568-9bb2-d7966413a1e7 · outbound
Unitary Categorical Symmetries Drinfeld, Quasi-Hopf algebras, Algebra i Analiz 6 (1989) 114–148
Reference 78
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Observation 89070bf8-db09-4572-ba46-046e75a6b17f · outbound
Unitary Categorical Symmetries Majid, Doubles of quasitriangular hopf algebras , Communications in Algebra 19 (1991) 3061–3073
Reference 79
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Observation 3ad9aa87-4d2f-466f-b65e-254aa295a3ad · outbound
Unitary Categorical Symmetries Roche, V
Reference 80
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Observation 703ed19d-5956-4c34-bb0d-5cf6f6e15b5d · outbound
Unitary Categorical Symmetries Davydov and D
Reference 81
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Observation 5aec6362-26f9-4522-9a51-46a19c1dfa69 · outbound
Unitary Categorical Symmetries Willerton, The twisted Drinfeld double of a finite group via gerbes and finite groupoids , Algebr
Reference 82
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Observation f823ebed-e5c6-4441-a190-504a54403ccc · outbound
Unitary Categorical Symmetries Tambara and S
Reference 83
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Observation 3d8c59e1-f837-4cec-a3b4-af99818dc0df · outbound
Unitary Categorical Symmetries Centers of graded fusion categories
Reference 84
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Unavailable: canonical work link unavailable.
Observation 5a14971d-0187-4dba-aa35-297df6df84c3 · outbound
Unitary Categorical Symmetries Topological Defect Lines and Renormalization Group Flows in Two Dimensions
Reference 85
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Observation 648bc614-d793-426f-b77b-1131036462be · outbound
Unitary Categorical Symmetries Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
Reference 86
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Observation 06a6e75a-43e7-4ddf-9957-9d3c6d797ec8 · outbound
Unitary Categorical Symmetries Commutative Algebras in Fibonacci Categories
Reference 87
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Observation 3c15e50f-c255-47c8-a01e-ff9172eb70e1 · outbound
Reference 88
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Observation 2c413e68-51de-4533-890f-165c36e6bf7e · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 89
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Observation 9fca1c95-b7e5-4fae-be98-86e5151f0bb5 · outbound
Unitary Categorical Symmetries Higher-Dimensional Algebra II: 2-Hilbert Spaces
Reference 90
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Observation d0e00769-ae2d-42fa-8d14-4000f6d60e53 · outbound
Unitary Categorical Symmetries The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
Reference 91
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Observation debec216-2467-4fdf-b17b-5adb82b4e47c · outbound
Unitary Categorical Symmetries Representation and character theory in 2-categories
Reference 92
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Observation a0237ab5-e636-4ee2-b1a1-93b7bfc83f5f · outbound
Unitary Categorical Symmetries Representation theory of 2-groups on finite dimensional 2-vector spaces
Reference 93
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d9ed741d-684c-49d2-be62-3fd3ee751b29 · outbound
Unitary Categorical Symmetries Explicit Formulas for 2-Characters
Reference 94
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1b5c03bc-94a6-427a-879e-7183c980b35a · outbound
Unitary Categorical Symmetries Non-invertible Symmetries and Higher Representation Theory I
Reference 95
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 27b9618a-f1fd-424e-a553-713d819f4730 · outbound
Unitary Categorical Symmetries Universal Non-Invertible Symmetries
Reference 96
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5ef06bda-cdbc-4285-8bda-d9dfdfb7b737 · outbound
Unitary Categorical Symmetries Non-invertible Symmetries and Higher Representation Theory II
Reference 97
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4e2a8250-5da8-4d35-a81a-6053cbfd904d · outbound
Unitary Categorical Symmetries Unifying Constructions of Non-Invertible Symmetries
Reference 98
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Unavailable: canonical work link unavailable.
Observation 0156dea5-8463-4fbd-8068-d910f7f5c7a8 · outbound
Reference 99
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Unavailable: canonical work link unavailable.
Observation a80947aa-7bd0-4e93-a9dc-31b9907ad9ad · outbound
Unitary Categorical Symmetries Unresolved cited work
Reference 100
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0ea11b1d-2c1e-42f5-9358-7a245b845c80 · inbound
Unitary Categorical Symmetries Unitary Categorical Symmetries
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.