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Invertible braided tensor categories

Adrien Brochier, David Jordan, Pavel Safronov and Noah Snyder

Algebraic & Geometric Topology 21 (2021) 2107–2140
Bibliography
1 M Araújo, Coherence for 3–dualizable objects, PhD thesis, University of Oxford (2017)
2 D Ayala, J Francis, Factorization homology of topological manifolds, J. Topol. 8 (2015) 1045 MR3431668
3 D Ayala, J Francis, The cobordism hypothesis, preprint (2017) arXiv:1705.02240
4 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
5 M Bärenz, J Barrett, Dichromatic state sum models for four-manifolds from pivotal functors, Comm. Math. Phys. 360 (2018) 663 MR3800795
6 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
7 D Ben-Zvi, A Brochier, D Jordan, Quantum character varieties and braided module categories, Selecta Math. 24 (2018) 4711 MR3874702
8 D Ben-Zvi, D Nadler, The character theory of a complex group, preprint (2009) arXiv:0904.1247
9 J E Bergner, Models for (,n)–categories and the cobordism hypothesis, from: "Mathematical foundations of quantum field theory and perturbative string theory" (editors H Sati, U Schreiber), Proc. Sympos. Pure Math. 83, Amer. Math. Soc. (2011) 17 MR2742424
10 M Brandenburg, A Chirvasitu, T Johnson-Freyd, Reflexivity and dualizability in categorified linear algebra, Theory Appl. Categ. 30 (2015) 808 MR3361309
11 A Brochier, D Jordan, N Snyder, On dualizability of braided tensor categories, preprint (2018) arXiv:1804.07538
12 A Bruguières, A Virelizier, Quantum double of Hopf monads and categorical centers, Trans. Amer. Math. Soc. 364 (2012) 1225 MR2869176
13 D Calaque, C I Scheimbauer, Factorization homology as a fully extended topological field theory, in preparation
14 F Costantino, N Geer, B Patureau-Mirand, Quantum invariants of 3–manifolds via link surgery presentations and non-semi-simple categories, J. Topol. 7 (2014) 1005 MR3286896
15 L Crane, L H Kauffman, D N Yetter, State-sum invariants of 4–manifolds, J. Knot Theory Ramifications 6 (1997) 177 MR1452438
16 L Crane, D Yetter, A categorical construction of 4D topological quantum field theories, from: "Quantum topology" (editors L H Kauffman, R A Baadhio), Ser. Knots Everything 3, World Sci. (1993) 120 MR1273569
17 A Davydov, M Müger, D Nikshych, V Ostrik, The Witt group of non-degenerate braided fusion categories, J. Reine Angew. Math. 677 (2013) 135 MR3039775
18 M De Renzi, A M Gainutdinov, N Geer, B Patureau-Mirand, I Runkel, 3–dimensional TQFTs from non-semisimple modular categories, preprint (2019) arXiv:1912.02063
19 A Debray, S Galatius, M Palmer, Lectures on invertible field theories, preprint (2019) arXiv:1912.08706
20 F DeMeyer, E Ingraham, Separable algebras over commutative rings, 181, Springer (1971) MR0280479
21 C L Douglas, C Schommer-Pries, N Snyder, Dualizable tensor categories, 1308, Amer. Math. Soc. (2020) MR4254952
22 G Dunn, Tensor product of operads and iterated loop spaces, J. Pure Appl. Algebra 50 (1988) 237 MR938617
23 P Etingof, S Gelaki, D Nikshych, V Ostrik, Tensor categories, 205, Amer. Math. Soc. (2015) MR3242743
24 P Etingof, D Nikshych, V Ostrik, An analogue of Radford’s S4 formula for finite tensor categories, Int. Math. Res. Not. 2004 (2004) 2915 MR2097289
25 P Etingof, V Ostrik, Finite tensor categories, Mosc. Math. J. 4 (2004) 627 MR2119143
26 V Farsad, A M Gainutdinov, I Runkel, SL(2, )–action for ribbon quasi-Hopf algebras, J. Algebra 522 (2019) 243 MR3897452
27 Z Fiedorowicz, R M Vogt, An additivity theorem for the interchange of En structures, Adv. Math. 273 (2015) 421 MR3311768
28 J Francis, The tangent complex and Hochschild cohomology of En–rings, Compos. Math. 149 (2013) 430 MR3040746
29 D Freed, 3–Dimensional TQFTs through the lens of the cobordism hypothesis, lecture slides (2012)
30 D Freed, 432876, lecture slides (2012)
31 D S Freed, The cobordism hypothesis, Bull. Amer. Math. Soc. 50 (2013) 57 MR2994995
32 D S Freed, Anomalies and invertible field theories, from: "String-Math 2013" (editors R Donagi, M R Douglas, L Kamenova, M Roček), Proc. Sympos. Pure Math. 88, Amer. Math. Soc. (2014) 25 MR3330283
33 G Ginot, Notes on factorization algebras, factorization homology and applications, from: "Mathematical aspects of quantum field theories" (editors D Calaque, T Strobl), Springer (2015) 429 MR3330249
34 S Gunningham, D Jordan, P Safronov, The finiteness conjecture for skein modules, preprint (2019) arXiv:1908.05233
35 O Gwilliam, C Scheimbauer, Duals and adjoints in higher Morita categories, preprint (2018) arXiv:1804.10924
36 R Haugseng, The higher Morita category of En–algebras, Geom. Topol. 21 (2017) 1631 MR3650080
37 G Janelidze, G M Kelly, A note on actions of a monoidal category, Theory Appl. Categ. 9 (2001) 61 MR1897810
38 T Johnson-Freyd, On the classification of topological orders, preprint (2020) arXiv:2003.06663
39 T Johnson-Freyd, C Scheimbauer, (Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories, Adv. Math. 307 (2017) 147 MR3590516
40 N Johnson, Azumaya objects in triangulated bicategories, J. Homotopy Relat. Struct. 9 (2014) 465 MR3258690
41 C Jones, S Morrison, D Penneys, J Plavnik, Extension theory for braided-enriched fusion categories, preprint (2019) arXiv:1910.03178
42 A Kirillov Jr., Y H Tham, Factorization homology and 4D TQFT, preprint (2020) arXiv:2002.08571
43 R Laugwitz, The relative monoidal center and tensor products of monoidal categories, Commun. Contemp. Math. 22 (2020) MR4142329
44 S Lentner, T Ohrmann, Factorizable R–matrices for small quantum groups, Symm. Integr. Geom. Methods Appl. 13 (2017) MR3705499
45 J Lurie, On the classification of topological field theories, from: "Current developments in mathematics" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), International (2009) 129 MR2555928
46 J Lurie, Higher algebra, preprint (2017)
47 V Lyubashenko, Modular transformations for tensor categories, J. Pure Appl. Algebra 98 (1995) 279 MR1324034
48 V Lyubashenko, S Majid, Braided groups and quantum Fourier transform, J. Algebra 166 (1994) 506 MR1280590
49 B Pareigis, Non-additive ring and module theory, IV : The Brauer group of a symmetric monoidal category, from: "Brauer groups" (editor D Zelinsky), Lecture Notes in Math. 549, Springer (1976) 112 MR0498794
50 P Pstrągowski, On dualizable objects in monoidal bicategories, framed surfaces and the cobordism hypothesis, preprint (2014) arXiv:1411.6691
51 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
52 J Roberts, S Willerton, On the Rozansky–Witten weight systems, Algebr. Geom. Topol. 10 (2010) 1455 MR2661534
53 M Rosso, Quantum groups at a root of 1 and tangle invariants, Int. J. Modern Phys. B 7 (1993) 3715 MR1241466
54 L Rozansky, E Witten, Hyper-Kähler geometry and invariants of three-manifolds, Selecta Math. 3 (1997) 401 MR1481135
55 C I Scheimbauer, Factorization homology as a fully extended topological field theory, PhD thesis, ETH Zürich (2014)
56 C Schommer-Pries, Invertible topological field theories, preprint (2017) arXiv:1712.08029
57 C J Schommer-Pries, Tori detect invertibility of topological field theories, Geom. Topol. 22 (2018) 2713 MR3811769
58 K Shimizu, Non-degeneracy conditions for braided finite tensor categories, Adv. Math. 355 (2019) MR3996323
59 K Shimizu, Further results on the structure of (co)ends in finite tensor categories, Appl. Categ. Structures 28 (2020) 237 MR4077241
60 U Tillmann, S–structures for k–linear categories and the definition of a modular functor, J. Lond. Math. Soc. 58 (1998) 208 MR1670122
61 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
62 E M Vitale, The Brauer and Brauer–Taylor groups of a symmetric monoidal category, Cahiers Topologie Géom. Différentielle Catég. 37 (1996) 91 MR1394505
63 K Walker, TQFTs, book project (2006)
64 K Walker, Premodular TQFTs, lecture slides (2014)
65 K Walker, Z Wang, (3+1)–TQFTs and topological insulators, Front. Phys. 7 (2012) 150
66 T A Wasserman, The Drinfeld centre of a symmetric fusion category is 2–fold monoidal, Adv. Math. 366 (2020) MR4072794
67 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772