Homotopy locally presentable enriched categories

Stephen Lack and Jiri Rosicky

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 homotopy 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.

Keywords: monoidal model category, enriched model category, weighted homotopy colimit, locally presentable category

2010 MSC: 18G55, 55U35, 18D20,18C35

Theory and Applications of Categories, Vol. 31, 2016, No. 25, pp 712-754.

Published 2016-08-02.

http://www.tac.mta.ca/tac/volumes/31/25/31-25.pdf

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