Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 805-846 |
| Number of pages | 42 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 64 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sept 2013 |
Bibliographical note
Funding Information:The first author benefitted from support from the French National Agency for Research (ANR grants HODAG and HOGT), while visits by the second author to France were partially supported by a Descartes-Huygens Prize of the Académie des Sciences.
Funding
The first author benefitted from support from the French National Agency for Research (ANR grants HODAG and HOGT), while visits by the second author to France were partially supported by a Descartes-Huygens Prize of the Académie des Sciences.