Algebraic & Geometric Topology Volume 24, issue 7 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

An explicit comparison between $2$–complicial sets and $\Theta_2$–spaces

Julia E Bergner, Viktoriya Ozornova and Martina Rovelli

Algebraic & Geometric Topology 24 (2024) 3827–3873

DOI: 10.2140/agt.2024.24.3827

Bibliography

1	D Ara, Higher quasi-categories vs higher Rezk spaces, J. K–Theory 14 (2014) 701 MR3350089
2	D Ara, G Maltsiniotis, Joint et tranches pour les ∞–catégories strictes, 165, Soc. Math. France (2020) MR4146146
3	C Barwick, (∞,n)–Cat as a closed model category, PhD thesis, University of Pennsylvania (2005) MR2706984
4	C Berger, Iterated wreath product of the simplex category and iterated loop spaces, Adv. Math. 213 (2007) 230 MR2331244
5	J E Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007) 397 MR2321038
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, A characterization of fibrant Segal categories, Proc. Amer. Math. Soc. 135 (2007) 4031 MR2341955
8	J E Bergner, C Rezk, Comparison of models for (∞,n)–categories, I, Geom. Topol. 17 (2013) 2163 MR3109865
9	J E Bergner, C Rezk, Comparison of models for (∞,n)–categories, II, J. Topol. 13 (2020) 1554 MR4186138
10	F Borceux, Handbook of categorical algebra, I: Basic category theory, 50, Cambridge Univ. Press (1994) MR1291599
11	A Campbell, Equivalences of complicial sets, handwritten notes (2019)
12	A Campbell, A homotopy coherent cellular nerve for bicategories, Adv. Math. 368 (2020) 107138 MR4088416
13	D Dugger, Universal homotopy theories, Adv. Math. 164 (2001) 144 MR1870515
14	J W Duskin, Simplicial matrices and the nerves of weak n–categories, I : Nerves of bicategories, Theory Appl. Categ. 9 (2001) 198 MR1897816
15	A Gagna, Y Harpaz, E Lanari, On the equivalence of all models for (∞,2)–categories, J. Lond. Math. Soc. 106 (2022) 1920 MR4498545
16	A Gagna, V Ozornova, M Rovelli, Nerves and cones of free loop-free ω–categories, Tunis. J. Math. 5 (2023) 273 MR4596736
17	D Gepner, R Haugseng, Enriched ∞–categories via non-symmetric ∞–operads, Adv. Math. 279 (2015) 575 MR3345192
18	R Haugseng, On lax transformations, adjunctions, and monads in (∞,2)–categories, High. Struct. 5 (2021) 244 MR4367222
19	V Hinich, Dwyer–Kan localization revisited, Homology Homotopy Appl. 18 (2016) 27 MR3460765
20	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
21	P S Hirschhorn, Overcategories and undercategories of cofibrantly generated model categories, J. Homotopy Relat. Struct. 16 (2021) 753 MR4343079
22	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
23	A Joyal, Disks, duality and Θ–categories, preprint (1997)
24	A Joyal, Quasi-categories vs simplicial categories, preprint (2007)
25	A Joyal, The theory of quasi-categories and its applications, preprint (2008)
26	A Joyal, M Tierney, Quasi-categories vs Segal spaces, from: "Categories in algebra, geometry and mathematical physics", Contemp. Math. 431, Amer. Math. Soc. (2007) 277 MR2342834
27	S Lack, A Quillen model structure for 2–categories, K–Theory 26 (2002) 171 MR1931220
28	S Lack, A Quillen model structure for bicategories, K–Theory 33 (2004) 185 MR2138540
29	T Lawson, Localization of enriched categories and cubical sets, Theory Appl. Categ. 32 (2017) 35 MR3695491
30	F Loubaton, Dualities in the complicial model of ∞–categories, preprint (2022) arXiv:2203.11845
31	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
32	J Lurie, (∞,2)–categories and the Goodwillie calculus, I, preprint (2009) arXiv:0905.0462
33	L Moser, V Ozornova, M Rovelli, Model independence of (∞,2)–categorical nerves, preprint (2022) arXiv:2206.00660
34	M Olschok, Left determined model structures for locally presentable categories, Appl. Categ. Structures 19 (2011) 901 MR2861071
35	V Ozornova, M Rovelli, Model structures for (∞,n)–categories on (pre)stratified simplicial sets and prestratified simplicial spaces, Algebr. Geom. Topol. 20 (2020) 1543 MR4105558
36	V Ozornova, M Rovelli, Nerves of 2–categories and 2–categorification of (∞,2)–categories, Adv. Math. 391 (2021) 107948 MR4301487
37	R Pellissier, Categories enrichies faibles, PhD thesis, Université de Nice Sophia Antipolis (2002) arXiv:math/0308246
38	C Rezk, A model category for categories, preprint (1996)
39	C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
40	C Rezk, A Cartesian presentation of weak n–categories, Geom. Topol. 14 (2010) 521 MR2578310
41	C Rezk, Introduction to quasicategories, (2022)
42	E Riehl, Complicial sets: an overture, from: "2016 MATRIX annals", MATRIX Book Ser. 1, Springer (2018) 49 MR3792516
43	E Riehl, D Verity, Recognizing quasi-categorical limits and colimits in homotopy coherent nerves, Appl. Categ. Structures 28 (2020) 669 MR4114996
44	E Riehl, D Verity, Elements of ∞–category theory, 194, Cambridge Univ. Press (2022) MR4354541
45	R Street, The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987) 283 MR920944
46	D Verity, Complicial sets characterising the simplicial nerves of strict ω–categories, 905, Amer. Math. Soc. (2008) MR2399898
47	D R B Verity, Weak complicial sets, I : Basic homotopy theory, Adv. Math. 219 (2008) 1081 MR2450607