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arXiv:1201.2134 [math.AT]AbstractReferencesReviewsResources

On the homotopy theory of enriched categories

Clemens Berger, Ieke Moerdijk

Published 2012-01-10, updated 2013-04-08Version 3

We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dg- and spectral categories. Our proof is mainly based on a fundamental property of cofibrant enriched categories on two objects, stated below as the Interval Cofibrancy Theorem.

Comments: v3: statement of Lemma 2.15 corrected
Categories: math.AT, math.CT
Subjects: 55U35, 18D20
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