ON THE HOMOTOPY THEORY OF ENRICHED CATEGORIES
Copyright policy )ON THE HOMOTOPY THEORY OF ENRICHED CATEGORIES
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.
v3: statement of Lemma 2.15 corrected
- Nice Sophia Antipolis University France
- Centre Hospitalier Universitaire de Nice France
- Université Côte d'Azur France
- Radboud University Nijmegen Netherlands
- Utrecht University Netherlands
Algebra and Topology, Quillen model structure, Mathematics - Category Theory, [MATH] Mathematics [math], enriched category, abstract homotopy theory, 55U35, 18D20, FOS: Mathematics, Algebraic Topology (math.AT), Category Theory (math.CT), Mathematics - Algebraic Topology, Algebra en Topologie, interval
Algebra and Topology, Quillen model structure, Mathematics - Category Theory, [MATH] Mathematics [math], enriched category, abstract homotopy theory, 55U35, 18D20, FOS: Mathematics, Algebraic Topology (math.AT), Category Theory (math.CT), Mathematics - Algebraic Topology, Algebra en Topologie, interval
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