Simplicial structures on model categories and functors

Details Simplicial structures on model categories and functors Simplicial structures on model categories and functors

2001-01-19

arxiv.org/abs/math/0101162v1

Mathematics

Algebraic Topology

To appear in American Journal of Mathematics

Scientific paper

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.

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