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Journal Article
Simplicial Structures on Model Categories and Functors
Charles Rezk, Stefan Schwede and Brooke Shipley
American Journal of Mathematics
Vol. 123, No. 3 (Jun., 2001), pp. 551-575
Published
by: The Johns Hopkins University Press
https://www.jstor.org/stable/25099071
Page Count: 25
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Topics: Functors, Adjoints, Equivalence relation, Mathematical theorems, Property rights, Axioms, Algebra, Factorization, Uniqueness
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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.
American Journal of Mathematics
© 2001 The Johns Hopkins University Press