Abstract

The primary aim of this work is an intrinsic homotopy theory of strict ω-categories. We establish a model structure on ωCat, the category of strict ω-categories. The constructions leading to the model structure in question are expressed entirely within the scope of ωCat, building on a set of generating cofibrations and a class of weak equivalences as basic items. All object are fibrant while free objects are cofibrant. We further exhibit model structures of this type on n-categories for arbitrary n ∈ N, as specialisations of the ω-categorical one along right adjoints. In particular, known cases for n = 1 and n = 2 nicely fit into the scheme.

Citations