A Quillen model structure for Gray-categories

Stephen Lack*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    11 Citations (Scopus)


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 This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types.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

    Original languageEnglish
    Pages (from-to)183-221
    Number of pages39
    JournalJournal of K-Theory
    Issue number2
    Publication statusPublished - Oct 2011

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