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Results tagged with simplicial-presheaves
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user 20233
A simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets).
6
votes
Accepted
Does the kan extension preserves contractible presheaves?
$f_!(X)$ is a cofibrant replacement of $*$ if and only if the comma category $f/d$ has a weakly contractible classifying space, for all $d\in D$.
Indeed, the value of $f_!(X)$ on $d$ is weakly equiva …
- 8,972
10
votes
Accepted
Homotopy left-exactness of a left derived functor
I do not know the answer for a general Quillen adjunction, but I will attempt to give a complete answer in the case you're interested in, when the adjunction $(F,G)$ is of the form $(f_!,f^\ast)$ for …
- 8,972