Simplicial structures on model categories and functors

Charles Rezk, Stefan Schwede, Brooke Shipley

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)551-575
Number of pages25
JournalAmerican Journal of Mathematics
Issue number3
StatePublished - Jun 2001
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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