ON THE HOMOTOPY THEORY OF ENRICHED CATEGORIES

Clemens Berger (1) , Ieke Moerdijk (2)

1 UNS UFR Sciences - Université Nice Sophia Antipolis - Faculté des Sciences
2 Institute for Mathematics, Astrophysics, and Particle Physics

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.

Mots clés: abstract homotopy theory; Quillen model structure; interval; enriched category

Domaines: Mathématiques [math]

Clemens Berger, Ieke Moerdijk. ON THE HOMOTOPY THEORY OF ENRICHED CATEGORIES. Quarterly Journal of Mathematics, 2013, 64 (3), pp.805-846. ⟨10.1093/qmath/hat023⟩. ⟨hal-01145619⟩