A Quillen model structure for Gray-categories

Details A Quillen model structure for Gray-categories A Quillen model structure for Gray-categories

2010-01-14

arxiv.org/abs/1001.2366v2

J. K-theory 8:183-221, 2011

Mathematics

Category Theory

v2: fuller discussion of relationship with work of Berger; localizations are done directly with simplicial sets

Scientific paper

10.1017/is010008014jkt127

A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of Gray-groupoids. This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types. The model structure on Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of tricategories and strict homomorphisms of tricategories.

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