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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Comparison of models for $(\infty, n)$–categories, I

Julia E Bergner and Charles Rezk

Geometry & Topology 17 (2013) 2163–2202
Abstract

While many different models for (,1)–categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for (,n)–categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as (,n)–categories. Furthermore, we establish Quillen equivalences between them.

Keywords
$(\infty, n)$–categories, $\Theta_n$–spaces, enriched categories
Mathematical Subject Classification 2010
Primary: 55U40
Secondary: 55U35, 18D15, 18D20, 18G30, 18C10
References
Publication
Received: 17 April 2012
Revised: 18 March 2013
Accepted: 17 April 2013
Published: 19 July 2013
Proposed: Paul Goerss
Seconded: Peter Teichner, Ralph Cohen
Authors
Julia E Bergner
Department of Mathematics
University of California Riverside
900 University Avenue
Riverside, CA 92521
USA
http://www.math.ucr.edu/~jbergner/
Charles Rezk
Department of Mathematics
University of Illinois at Urbana-Champaign
273 Altgeld Hall
MC-382
1409 West Green Street
Urbana, IL 61801
USA
http://www.math.uiuc.edu/~rezk/