A cartesian presentation of weak n–categories

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 $Θ_{n}$ . This notion is a generalization of that of complete Segal spaces (which are precisely the $(\infty, 1)$ – $Θ$ –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

Volume 14, issue 1 (2010)

Charles Rezk

Abstract

Keywords

Mathematical Subject Classification 2000

References

Publication

Authors