A cartesian presentation of weak ncategories
Abstract
We propose a notion of weak (n+k,n)category, which we call (n+k,n)Thetaspaces. The (n+k,n)Thetaspaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal's category Theta_n. This notion is a generalization of that of complete Segal spaces (which are precisely the (infty,1)Thetaspaces). Our main result is that the above model category is cartesian.
 Publication:

arXiv eprints
 Pub Date:
 January 2009
 arXiv:
 arXiv:0901.3602
 Bibcode:
 2009arXiv0901.3602R
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Topology;
 18D05
 EPrint:
 Incorporates corrections to the published version, which appeared in a separate correction note