Injective and projective model structures on enriched diagram categories

In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local presentability, accessibility, and “acyclicity” conditions, using the methods of lifting model structures from an adjunction introduced by Garner, Hess, Kędziorek, Riehl, and Shipley.

Keywords

injective and projective model structure, enriched functor category, induced model structure

2010 Mathematics Subject Classification

18D20, 18G55, 55U35

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Received 13 November 2017

Received revised 30 November 2018

Published 13 March 2019