Algebraic & Geometric Topology Volume 21, issue 7 (2021)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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The Hochschild complex of a finite tensor category

Christoph Schweigert and Lukas Woike

Algebraic & Geometric Topology 21 (2021) 3689–3734

DOI: 10.2140/agt.2021.21.3689

Bibliography

1	B Bakalov, A Kirillov Jr., On the Lego–Teichmüller game, Transform. Groups 5 (2000) 207 MR1780935
2	B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, 21, Amer. Math. Soc. (2001) MR1797619
3	B Bartlett, C L Douglas, C J Schommer-Pries, J Vicary, Modular categories as representations of the 3–dimensional bordism 2–category, preprint (2015) arXiv:1509.06811
4	C Berger, I Moerdijk, The Boardman–Vogt resolution of operads in monoidal model categories, Topology 45 (2006) 807 MR2248514
5	C Cibils, M J Redondo, Cartan–Leray spectral sequence for Galois coverings of linear categories, J. Algebra 284 (2005) 310 MR2115017
6	R Dijkgraaf, E Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393 MR1048699
7	C L Douglas, C Schommer-Pries, N Snyder, The balanced tensor product of module categories, Kyoto J. Math. 59 (2019) 167 MR3934626
8	P Etingof, S Gelaki, D Nikshych, V Ostrik, Tensor categories, 205, Amer. Math. Soc. (2015) MR3242743
9	P Etingof, V Ostrik, Finite tensor categories, Mosc. Math. J. 4 (2004) 627 MR2119143
10	D S Freed, F Quinn, Chern–Simons theory with finite gauge group, Comm. Math. Phys. 156 (1993) 435 MR1240583
11	B Fresse, Homotopy of operads and Grothendieck–Teichmüller groups, I : The algebraic theory and its topological background, 217, Amer. Math. Soc. (2017) MR3643404
12	J Fuchs, C Schweigert, Coends in conformal field theory, from: "Lie algebras, vertex operator algebras, and related topics" (editors K Barron, E Jurisich, A Milas, K Misra), Contemp. Math. 695, Amer. Math. Soc. (2017) 65 MR3709706
13	J Fuchs, C Schweigert, A Valentino, Bicategories for boundary conditions and for surface defects in 3–d TFT, Comm. Math. Phys. 321 (2013) 543 MR3063919
14	C Galindo, Coherence for monoidal G–categories and braided G–crossed categories, J. Algebra 487 (2017) 118 MR3671186
15	N Geer, J Kujawa, B Patureau-Mirand, M–traces in (non-unimodular) pivotal categories, Algebr. Represent. Theory (2021)
16	S Gelaki, D Naidu, D Nikshych, Centers of graded fusion categories, Algebra Number Theory 3 (2009) 959 MR2587410
17	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
18	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
19	E Hoefel, OCHA and the Swiss-cheese operad, J. Homotopy Relat. Struct. 4 (2009) 123 MR2520990
20	G Horel, Factorization homology and calculus à la Kontsevich Soibelman, J. Noncommut. Geom. 11 (2017) 703 MR3669116
21	Y Z Huang, Rigidity and modularity of vertex tensor categories, Commun. Contemp. Math. 10 (2008) 871 MR2468370
22	N Idrissi, Swiss-cheese operad and Drinfeld center, Israel J. Math. 221 (2017) 941 MR3704940
23	B Iversen, Cohomology of sheaves, Springer (1986) MR842190
24	H Kajiura, J Stasheff, Homotopy algebras inspired by classical open-closed string field theory, Comm. Math. Phys. 263 (2006) 553 MR2211816
25	C Kassel, Quantum groups, 155, Springer (1995) MR1321145
26	B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
27	T Kerler, V V Lyubashenko, Non-semisimple topological quantum field theories for 3–manifolds with corners, 1765, Springer (2001) MR1862634
28	A Kirillov Jr, On G–equivariant modular categories, preprint (2004) arXiv:math/0401119
29	S Lentner, S N Mierach, C Schweigert, Y Sommerhäuser, Hochschild cohomology and the modular group, J. Algebra 507 (2018) 400 MR3807053
30	S Lentner, S N Mierach, C Schweigert, Y Sommerhäuser, Hochschild cohomology, modular tensor categories, and mapping class groups, (2020) arXiv:2003.06527
31	V V Lyubashenko, Invariants of 3–manifolds and projective representations of mapping class groups via quantum groups at roots of unity, Comm. Math. Phys. 172 (1995) 467 MR1354257
32	V Lyubashenko, Modular transformations for tensor categories, J. Pure Appl. Algebra 98 (1995) 279 MR1324034
33	V Lyubashenko, Ribbon abelian categories as modular categories, J. Knot Theory Ramifications 5 (1996) 311 MR1405715
34	V Lyubashenko, S Majid, Braided groups and quantum Fourier transform, J. Algebra 166 (1994) 506 MR1280590
35	S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR0354798
36	J Maier, T Nikolaus, C Schweigert, Equivariant modular categories via Dijkgraaf–Witten theory, Adv. Theor. Math. Phys. 16 (2012) 289 MR3019407
37	R McCarthy, The cyclic homology of an exact category, J. Pure Appl. Algebra 93 (1994) 251 MR1275967
38	M Müger, Galois extensions of braided tensor categories and braided crossed G–categories, J. Algebra 277 (2004) 256 MR2059630
39	L Müller, L Woike, Equivariant higher Hochschild homology and topological field theories, Homology Homotopy Appl. 22 (2020) 27 MR4013454
40	L Müller, L Woike, The little bundles operad, Algebr. Geom. Topol. 20 (2020) 2029 MR4127089
41	N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
42	N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
43	E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
44	E Riehl, Homotopy coherent structures, lecture notes (2018) arXiv:1801.07404
45	P Salvatore, N Wahl, Framed discs operads and Batalin–Vilkovisky algebras, Q. J. Math. 54 (2003) 213 MR1989873
46	C Schweigert, L Woike, Extended homotopy quantum field theories and their orbifoldization, J. Pure Appl. Algebra 224 (2020) MR4021927
47	K Shimizu, Non-degeneracy conditions for braided finite tensor categories, Adv. Math. 355 (2019) MR3996323
48	K Shimizu, Further results on the structure of (co)ends in finite tensor categories, Appl. Categ. Structures 28 (2020) 237 MR4077241
49	M Shulman, Homotopy limits and colimits and enriched homotopy theory, preprint (2006) arXiv:math/0610194
50	Y Sommerhäuser, Y Zhu, Hopf algebras and congruence subgroups, 1028, Amer. Math. Soc. (2012) MR2985696
51	V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
52	V Turaev, Homotopy field theory in dimension 3 and crossed group-categories, preprint (2000) arXiv:math/0005291
53	V Turaev, Homotopy quantum field theory, 10, Eur. Math. Soc. (2010) MR2674592
54	V Turaev, A Virelizier, On 3–dimensional homotopy quantum field theory, I, Int. J. Math. 23 (2012) MR2959440
55	V Turaev, A Virelizier, On 3–dimensional homotopy quantum field theory, II : The surgery approach, Int. J. Math. 25 (2014) MR3195545
56	A A Voronov, The Swiss-cheese operad, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 365 MR1718089
57	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324