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Pushouts of Dwyer maps are $(\infty,1)$–categorical

Philip Hackney, Viktoriya Ozornova, Emily Riehl and Martina Rovelli

Algebraic & Geometric Topology 24 (2024) 2171–2183
Bibliography
1 D Ara, G Maltsiniotis, Vers une structure de catégorie de modèles à la Thomason sur la catégorie des n–catégories strictes, Adv. Math. 259 (2014) 557 MR3197667
2 C Barwick, D M Kan, Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. 23 (2012) 42 MR2877401
3 M A Batanin, C Berger, Homotopy theory for algebras over polynomial monads, Theory Appl. Categ. 32 (2017) 148 MR3607212
4 J E Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007) 2043 MR2276611
5 A M Bohmann, K Mazur, A M Osorno, V Ozornova, K Ponto, C Yarnall, A model structure on G𝒞at, from: "Women in topology: collaborations in homotopy theory" (editors M Basterra, K Bauer, K Hess, B Johnson), Contemp. Math. 641, Amer. Math. Soc. (2015) 123 MR3380072
6 A Campbell, A counterexample in quasi-category theory, Proc. Amer. Math. Soc. 148 (2020) 37 MR4042827
7 D C Cisinski, La classe des morphismes de Dwyer n’est pas stable par retractes, Cahiers Topologie Géom. Différentielle Catég. 40 (1999) 227 MR1716777
8 W G Dwyer, D M Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980) 267 MR0579087
9 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
10 Z Fiedorowicz, A counterexample to a group completion conjecture of J C Moore, Algebr. Geom. Topol. 2 (2002) 33 MR1885214
11 P Hackney, V Ozornova, E Riehl, M Rovelli, Pushouts of Dwyer maps are (,1)–categorical, (2022) arXiv:2205.02353v2
12 P Hackney, V Ozornova, E Riehl, M Rovelli, An (,2)–categorical pasting theorem, Trans. Amer. Math. Soc. 376 (2023) 555 MR4510118
13 M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. 184 (2016) 1 MR3505179
14 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
15 A Joyal, The theory of quasi-categories and its applications, preprint (2008)
16 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
17 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
18 J Lurie, (,2)–categories and the Goodwillie calculus, I, preprint (2009) arXiv:0905.0462
19 D McDuff, On the classifying spaces of discrete monoids, Topology 18 (1979) 313 MR0551013
20 S Schwede, Categories and orbispaces, Algebr. Geom. Topol. 19 (2019) 3171 MR4023338
21 D Stevenson, Covariant model structures and simplicial localization, North-West. Eur. J. Math. 3 (2017) 141 MR3683375
22 D Stevenson, Model structures for correspondences and bifibrations, preprint (2018) arXiv:1807.08226
23 D Stevenson, Notes on the Joyal model structure, preprint (2018) arXiv:1810.05233
24 R W Thomason, Cat as a closed model category, Cahiers Topologie Géom. Différentielle 21 (1980) 305 MR0591388