Subject: Re: two questions From: "Clark Barwick" Date: Tue, 22 May 2007 15:23:30 +0200 Hi, This is in response to P. Gaucher's second question. The only place I know where anything like this is written up with a full proof is in an appendix to Jacob's higher topos theory paper, at his Harvard website: http://www.math.harvard.edu/~lurie/ His Proposition A.3.3.3 is exactly your statement, except that he assumes that C is a simplicial model category, that I is a simplicial category, and that C^I is of course the category of simplicially enriched functors I --> C. Of course he also shows that the resulting model category is simplicial. (I seem to recall that in an earlier version of the book, Lurie's statement is exactly the same as yours.) Hope that helps. -- Clark Barwick Matematisk Institutt Universitetet i Oslo Boks 1053 Blindern NO 0316 Oslo Norway Tel: +47 22 85 59 12 Fax: +47 22 85 43 49 clarkbar@gmail.com clarkbar@math.uio.no http://folk.uio.no/clarkbar