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7
votes
1answer
238 views

Is there a practical criterion to determine whether the limit of a diagram of real chain complexes is also a homotopy limit?

Consider a diagram D: I→ChR of real connective chain complexes. In the example I have in mind all chain complexes are concentrated in some fixed degree n. There is a canonical map lim D → holim D ...
3
votes
0answers
142 views

Jardine model structure as left Bousfield localization

This should be a really basic question, but I'm stuck on it. The question. I see written everywhere (for example here, or in the article [DHI] Hypercovers and simplicial presheaves of Dugger, ...
4
votes
1answer
287 views

Homotopy left-exactness of a left derived functor

Let $$ F: \mathcal{C} \leftrightarrows \mathcal{D} :G $$ be a Quillen adjunction between model categories. Consider the corresponding adjunction of total derived functors $$ \mathbb{L}F: ...
4
votes
0answers
159 views

Is there a local projective model structure on simplicial sheaves? What are its fibrant objects?

Consider a site S (I am mostly interested in hypercomplete sites, e.g., the site of smooth manifolds). The category of simplicial presheaves SPSh(S) on S can be equipped with the local projective ...
5
votes
2answers
296 views

Necessary conditions for cofibrancy in global projective model structure on simplicial presheaves

Consider the global projective model category of simplicial presheaves on some category (the category of smooth manifolds is particularly interesting to me). In Section 9.1 of Dugger's paper ...