Simplicial structures on model categories and functors
Abstract
We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen equivalent to simplicial model categories. A simplicial model category provides higher order structure such as composable mapping spaces and homotopy colimits. We also show that certain homotopy invariant functors can be replaced by weakly equivalent simplicial, or `continuous', functors. This is used to show that if a simplicial model category structure exists on a model category then it is unique up to simplicial Quillen equivalence.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:math/0101162
 Bibcode:
 2001math......1162R
 Keywords:

 Mathematics  Algebraic Topology;
 55U35
 EPrint:
 To appear in American Journal of Mathematics