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