On the homotopy theory of enriched categories
By C. Berger, Ieke Moerdijk. 2012
67 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f29020b4285c59524c34680bb66387a560ec2737
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Homotopy theory for algebras over polynomial monads (2013, unknown): “[14]] A model category is called K-compactly generated if it is cofibrantly generated, its class of weak equivalences is K-perfect, and each object is small with respect to K.”
- Dwyer–Kan homotopy theory of enriched categories (2012, background): “odel category satisfying Schwede–Shipley’s monoid axiom [SS00, Definitions 3.3]. Then Cat(V ) admits the Dwyer–Kan model structure. Moreover, this model structure is combinatorial. Berger and Moerdijk [BM13] approach the problem of endowing Cat(V ) with a model structure in a different way. Trivial fib”