Homotopy locally presentable enriched categories

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 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 has all objects of V are cofibrant.