Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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