English

A cartesian presentation of weak n-categories

Category Theory 2014-11-11 v3 Algebraic Topology

Abstract

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.

Keywords

Cite

@article{arxiv.0901.3602,
  title  = {A cartesian presentation of weak n-categories},
  author = {Charles Rezk},
  journal= {arXiv preprint arXiv:0901.3602},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T12:03:51.298Z