Homotopy locally presentable enriched categories

Stephen Lack, Jiří Rosický

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    Abstract

    We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and ho-motopy local presentability. The main result, which was known for simplicially-enriched categories, links homotopy locally presentable V-categories with combinatorial model V-categories, in the case where all objects of V are cofibrant.

    Original languageEnglish
    Article number25
    Pages (from-to)712-754
    Number of pages43
    JournalTheory and Applications of Categories
    Volume31
    Publication statusPublished - 2 Aug 2016

    Keywords

    • monoidal model category
    • enriched model category
    • weighted homotopy colimit
    • locally presentable category

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