Replacing model categories with simplicial ones

Abstract:

Let M be a model category and C be a small indexing category. In this paper a model category structure is constructed on the diagram category M^C, where the weak equivalences are maps inducing weak equivalences on the homotopy colimit. (Certain hypotheses must be placed on M and C for this to work). When C is the category \Delta^op---so that M^C is the category of simplicial objects sM---we use this model structure to follow up an idea of Stefan Schwede and show that sM becomes a simplicial model category which is Quillen equivalent to M. Thus, we have a method for replacing any `reasonable' model category by a simplicial category which is Quillen equivalent to it.

• Dvi file , Trans. Amer. Math. Soc. vol. 353 (2001), #12, 5003-5027.