Volume 17, issue 4 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Comparison of models for $(\infty, n)$–categories, I

Julia E Bergner and Charles Rezk

Geometry & Topology 17 (2013) 2163–2202
Bibliography
1 D Ayala, N Rozenblyum, work in progress
2 B Badzioch, Algebraic theories in homotopy theory, Ann. of Math. 155 (2002) 895 MR1923968
3 C Barwick, Homotopy coherent algebra II: Iterated wreath products of $O$ and $(\infty, n)$–categories, In preparation
4 C Barwick, C Schommer-Pries, On the unicity of the homotopy theory of higher categories arXiv:1112.0040
5 T Beke, Sheafifiable homotopy model categories, II, J. Pure Appl. Algebra 164 (2001) 307 MR1857744
6 C Berger, Iterated wreath product of the simplex category and iterated loop spaces, Adv. Math. 213 (2007) 230 MR2331244
7 J E Bergner, Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006) 1925 MR2263055
8 J E Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007) 2043 MR2276611
9 J E Bergner, Simplicial monoids and Segal categories, 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) 59 MR2342822
10 J E Bergner, Three models for the homotopy theory of homotopy theories, Topology 46 (2007) 397 MR2321038
11 J E Bergner, A survey of $(\infty,1)$–categories, from: "Towards higher categories", IMA Vol. Math. Appl. 152, Springer (2010) 69 MR2664620
12 J E Bergner, C Rezk, Enriched Segal categories, In preparation
13 J E Bergner, C Rezk, Reedy categories and the $\varTheta$–construction, Math. Z. 274 (2013) 499 MR3054341
14 D Dugger, D I Spivak, Mapping spaces in quasicategories, Algebr. Geom. Topol. 11 (2011) 263 MR2764043
15 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
16 P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser (1999) MR1711612
17 P S Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs 99, American Mathematical Society (2003) MR1944041
18 A Hirschowitz, C Simpson, Descente pour les $n$–champs arXiv:math/9807049
19 M Hovey, Model categories, Mathematical Surveys and Monographs 63, American Mathematical Society (1999) MR1650134
20 A Joyal, Simplicial categories vs quasi-categories, In preparation
21 A Joyal, The theory of quasi-categories I, In preparation
22 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
23 J Jurie, $(\infty, 2)$–categories and Goodwillie calculus arXiv:math/09050462
24 J Lurie, Higher topos theory, Annals of Mathematics Studies 170, Princeton Univ. Press (2009) MR2522659
25 J Lurie, On the classification of topological field theories, from: "Current developments in mathematics, 2008" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), Int. Press, Somerville, MA (2009) 129 MR2555928
26 S Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics 5, Springer (1998) MR1712872
27 R Pellissier, Catégories enrichies faibles arXiv:math/0308246
28 D G Quillen, Homotopical algebra, Lecture Notes in Mathematics 43, Springer (1967) MR0223432
29 C L Reedy, Homotopy theory of model categories, Unpublished manuscript
30 C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
31 C Rezk, A Cartesian presentation of weak $n$–categories, Geom. Topol. 14 (2010) 521 MR2578310
32 C Simpson, Homotopy theory of higher categories, New Mathematical Monographs 19, Cambridge Univ. Press (2012) MR2883823
33 B Toën, Vers une axiomatisation de la théorie des catégories supérieures, $K$–Theory 34 (2005) 233 MR2182378
34 D R B Verity, Weak complicial sets, I: Basic homotopy theory, Adv. Math. 219 (2008) 1081 MR2450607