English

Simplicial structures on model categories and functors

Algebraic Topology 2020-01-13 v1

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.

Keywords

Cite

@article{arxiv.math/0101162,
  title  = {Simplicial structures on model categories and functors},
  author = {Charles Rezk and Stefan Schwede and Brooke Shipley},
  journal= {arXiv preprint arXiv:math/0101162},
  year   = {2020}
}

Comments

To appear in American Journal of Mathematics