On the homotopy theory of enriched categories
classification
🧮 math.AT
math.CT
keywords
categoriesenrichedmodelbelowcategorycofibrancycofibrantconditions
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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.
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