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.