Algebraic & Geometric Topology Volume 17, issue 2 (2017)

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

Homotopy theory of cocomplete quasicategories

Karol Szumiło

Algebraic & Geometric Topology 17 (2017) 765–791

DOI: 10.2140/agt.2017.17.765

Bibliography

1	C Barwick, D M Kan, A characterization of simplicial localization functors and a discussion of DK equivalences, Indag. Math. 23 (2012) 69 MR2877402
2	C Barwick, D M Kan, Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. 23 (2012) 42 MR2877401
3	C Barwick, C Schommer-Pries, On the unicity of the homotopy theory of higher categories, preprint (2013) arXiv:1112.0040v4
4	J E Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007) 397 MR2321038
5	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
6	K S Brown, Abstract homotopy theory and generalized sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973) 419 MR0341469
7	D C Cisinski, Catégories dérivables, Bull. Soc. Math. France 138 (2010) 317 MR2729017
8	D Dugger, D I Spivak, Mapping spaces in quasi-categories, Algebr. Geom. Topol. 11 (2011) 263 MR2764043
9	W G Dwyer, D M Kan, J H Smith, Homotopy commutative diagrams and their realizations, J. Pure Appl. Algebra 57 (1989) 5 MR984042
10	P Gabriel, M Zisman, Calculus of fractions and homotopy theory, , Springer (1967) MR0210125
11	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser, Basel (1999) MR1711612
12	A Hirschowitz, C Simpson, Descente pour les n–champs, preprint (2001) arXiv:math/9807049v3
13	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
14	A Joyal, The theory of quasi-categories and its applications, from: "Advanced course on simplicial methods in higher categories", Quaderns 45, CRM (2008) 149
15	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
16	J Lurie, Higher topos theory, 170, Princeton University Press (2009) MR2522659
17	D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
18	C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
19	E Riehl, D Verity, Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions, Homology Homotopy Appl. 17 (2015) 1 MR3338539
20	A Rădulescu-Banu, Cofibrations in homotopy theory, preprint (2009) arXiv:math/0610009v4
21	K Szumiło, Two models for the homotopy theory of cocomplete homotopy theories, PhD thesis, Rheinische Friedrich-Wilhelms-Universität Bonn (2014)
22	K Szumiło, Two models for the homotopy theory of cocomplete homotopy theories, preprint (2014) arXiv:1411.0303
23	K Szumiło, Frames in cofibration categories, J. Homotopy Relat. Struct. (2016) 1
24	K Szumiło, Homotopy theory of cofibration categories, Homology Homotopy Appl. 18 (2016) 345 MR3576003
25	B Toën, Vers une axiomatisation de la théorie des catégories supérieures, K–Theory 34 (2005) 233 MR2182378
26	R M Vogt, The HELP-lemma and its converse in Quillen model categories, J. Homotopy Relat. Struct. 6 (2011) 115 MR2818703
27	F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796