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