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A Quillen model structure for Gray-categories

Published online by Cambridge University Press:  24 September 2010

Stephen Lack
Stephen Lack
Affiliation:
School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797 Penrith South DC NSW 1797, Australia and Department of Mathematics, Macquarie University, NSW 2109, Australia. steve.lack@mq.edu.au
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Abstract

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 This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types.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.

Keywords

Gray-categoryenriched categoryQuillen model categoryhomotopy 3-types

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 2 , October 2011 , pp. 183 - 221
Copyright
Copyright © ISOPP 2010

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