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fianlly added the details of Dugger’s description of cofibrant objects in the projective model structure on simplicial presheaves in the section Cofibrant objects.
added more details on weak equivalences (local epimorphisms, really) in the Cech localization of the projective model structure from Dugger-Hollander-Isaksen
at model structure on simplicial presheaves I have (finally) added a section
Presentation of (oo,1)-toposes
I have also added to the section Homtopy (co)limits the observation that finite homotopy limits in the local model structure may be computed in the global structure.
have added also a section Inclusion of chain complexes of sheaves, so far just observing the obvious Quillen adjunction induced from Dold-Kan
I had had a section on descent for presheaves with coefficients in strict $\infty$-groupoids and how it relates to the descent of these regarded as simplicial presheaves over in the entry on smooth $\infty$-groupoids. Since it did not really belog there specifically at all, I have now moved that over to model structure on simplicial presheaves in a new section:
Descent for values in strict and abelian $\infty$-groupoids.
The main point is there a clear statement of Verity’s result of sufficient conditions under which Street’s definition of descent is actually correct and matches the one of simplicial presheaves.
(I have only copy-and-pasted it for the moment. I should go through this and see if there is need to polish or otherwise improve this.)
I have added publication data to
cross-linked the discussion of local right properness (here) with locally cartesian closed model category and with locally cartesian closed (infinity,1)-category
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