A cartesian presentation of weak n-categories

Details A cartesian presentation of weak n-categories A cartesian presentation of weak n-categories

2009-01-23

arxiv.org/abs/0901.3602v3

Geometry & Topology 14 (2010), 521-571; Geometry & Topology 14 (2010) 2301-2304

Mathematics

Category Theory

Incorporates corrections to the published version, which appeared in a separate correction note

Scientific paper

10.2140/gt.2010.14.521

We propose a notion of weak (n+k,n)-category, which we call (n+k,n)-Theta-spaces. The (n+k,n)-Theta-spaces 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)-Theta-spaces). Our main result is that the above model category is cartesian.

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