Algebraic & Geometric Topology Volume 25, issue 2 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Enriched quasicategories and the templicial homotopy coherent nerve

Wendy Lowen and Arne Mertens

Algebraic & Geometric Topology 25 (2025) 1029–1074

DOI: 10.2140/agt.2025.25.1029

Bibliography

1	M Aguiar, Internal categories and quantum groups, PhD thesis, Cornell University (1997) MR2696373
2	M Aguiar, S Mahajan, Monoidal functors, species and Hopf algebras, 29, Amer. Math. Soc. (2010) MR2724388
3	H V Bacard, Segal enriched categories and applications, Theory Appl. Categ. 35 (2020) 1227
4	H J Baues, Geometry of loop spaces and the cobar construction, 230, Amer. Math. Soc. (1980) MR567799
5	C Berger, I Moerdijk, On the homotopy theory of enriched categories, Q. J. Math. 64 (2013) 805 MR3094501
6	J E Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007) 2043 MR2276611
7	J E Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007) 397 MR2321038
8	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR420609
9	A K Bousfield, Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77) 207 MR478159
10	J M Cordier, Sur la notion de diagramme homotopiquement cohérent, Cahiers Topologie Géom. Différentielle 23 (1982) 93 MR648798
11	J M Cordier, T Porter, Vogt’s theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Philos. Soc. 100 (1986) 65 MR838654
12	B Day, On closed categories of functors, from: "Reports of the Midwest Category Seminar, IV" (editor S MacLane), Lecture Notes in Math. 137, Springer (1970) 1 MR272852
13	E Dimitriadis Bermejo, A new model for dg-categories, PhD thesis, Université de Toulouse (2022)
14	D Dugger, D I Spivak, Rigidification of quasi-categories, Algebr. Geom. Topol. 11 (2011) 225 MR2764042
15	S Eilenberg, J A Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. 51 (1950) 499 MR35434
16	D Gepner, R Haugseng, Enriched ∞-categories via non-symmetric ∞-operads, Adv. Math. 279 (2015) 575 MR3345192
17	H Gindi, Coherent nerves for higher quasicategories, Theory Appl. Categ. 37 (2021) 709 MR4276763
18	D Grady, D Pavlov, Extended field theories are local and have classifying spaces, preprint (2023) arXiv:2011.01208
19	R Haugseng, Rectification of enriched ∞-categories, Algebr. Geom. Topol. 15 (2015) 1931 MR3402334
20	A Hirschowitz, C Simpson, Descente pour les n-champs, preprint (2001) arXiv:math/9807049
21	A Joyal, Disks, duality, and Theta-categories, unpublished manuscript (1997)
22	A Joyal, Quasi-categories and Kan complexes, J. Pure Appl. Algebra 175 (2002) 207 MR1935979
23	A Joyal, Notes on quasi-categories, unpublished manuscript (2004)
24	A Joyal, Quasi-categories vs simplicial categories, unpublished manuscript (2007)
25	A Joyal, M Tierney, Quasi-categories vs Segal spaces, from: "Categories in algebra, geometry and mathematical physics" (editors A Davydov, M Batanin, M Johnson, S Lack, A Neeman), Contemp. Math. 431, Amer. Math. Soc. (2007) 277 MR2342834
26	T Leinster, Homotopy algebras for operads, preprint (2000) arXiv:math/0002180
27	W Lowen, A Mertens, Frobenius templicial modules and the dg-nerve, preprint (2023) arXiv:2005.04778
28	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
29	J Lurie, Higher algebra, preprint (2017)
30	J Lurie, Kerodon, online resource (2018)
31	S MacLane, Categories for the working mathematician, 5, Springer (1971) MR354798
32	A Mertens, Templicial objects: simplicial objects in a monoidal category, PhD thesis, University of Antwerp (2022)
33	A Mertens, Nerves of enriched categories via necklaces, preprint (2024) arXiv:2408.10049
34	L Moser, N Rasekh, M Rovelli, Homotopy coherent nerves of enriched categories, preprint (2022) arXiv:2208.02745
35	F Muro, Dwyer–Kan homotopy theory of enriched categories, J. Topol. 8 (2015) 377 MR3356766
36	D G Quillen, Homotopical algebra, 43, Springer (1967) MR223432
37	C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
38	E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
39	C Simpson, Homotopy theory of higher categories, 19, Cambridge Univ. Press (2012) MR2883823
40	A E Stanculescu, Constructing model categories with prescribed fibrant objects, Theory Appl. Categ. 29 (2014) 635 MR3274498
41	R Street, Elementary cosmoi, I, from: "Category seminar" (editor G M Kelly), Lecture Notes in Math. 420, Springer (1974) 134 MR354813