Volume 14, issue 1 (2010)

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

Volume 27
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

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
A cartesian presentation of weak $n$–categories

Charles Rezk

Geometry & Topology 14 (2010) 521–571

Erratum: Geometry & Topology 14 (2010) 2301–2304

Abstract

We propose a notion of weak (n + k,n)–category, which we call (n + k,n)Θ–spaces. The (n + k,n)Θ–spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal’s category  Θn. This notion is a generalization of that of complete Segal spaces (which are precisely the (,1)Θ–spaces). Our main result is that the above model category is cartesian.

Keywords
$n$–categories, complete Segal spaces
Mathematical Subject Classification 2000
Primary: 18D05
Secondary: 55U40
References
Publication
Received: 7 February 2009
Revised: 6 May 2009
Accepted: 16 September 2009
Preview posted: 3 November 2009
Published: 2 January 2010
Proposed: Ralph Cohen
Seconded: Haynes Miller, Peter Teichner
Authors
Charles Rezk
Department of Mathematics
University of Illinois at Urbana-Champaign
273 Altgeld Hall, MC-382
1409 W Green Street
Urbana, IL 61801