Dwyer-Kan homotopy theory of enriched categories
Fernando Muro
TL;DR
This paper develops a model structure for small categories enriched over certain monoidal model categories, establishing a framework for understanding homotopy theory in enriched categorical contexts.
Contribution
It introduces a model structure on enriched categories with Dwyer-Kan equivalences, extending homotopy theory to enriched categorical settings.
Findings
Constructed a model structure on enriched categories
Defined weak equivalences as Dwyer-Kan equivalences
Provided tools for homotopy theory in enriched categories
Abstract
We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer-Kan equivalences, i.e. enriched functors which induce weak equivalences on morphism objects and equivalences of ordinary categories when we take sets of connected components on morphism objects.
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