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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 25th 2010

fianlly added the details of Dugger’s description of cofibrant objects in the projective model structure on simplicial presheaves in the section Cofibrant objects.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 25th 2010

added more details on weak equivalences (local epimorphisms, really) in the Cech localization of the projective model structure from Dugger-Hollander-Isaksen

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 24th 2011
• (edited Jan 24th 2011)

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.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 24th 2011

have added also a section Inclusion of chain complexes of sheaves, so far just observing the obvious Quillen adjunction induced from Dold-Kan

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeFeb 1st 2011
• (edited Feb 1st 2011)

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:

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.)

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 2nd 2018

added pointer to the MO comment Garner 13 characterizing projectively cofibrant simplicial presheaves.

Somebody should spell out the details here! If only by copy-and-pasting-and-beautifying-a-little the code from the MO answer.

• CommentRowNumber7.
• CommentAuthorTim_Porter
• CommentTimeMar 29th 2019

Fixed some ?ech which should have been Čech.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 7th 2020

I have added publication data to

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJun 12th 2021
• (edited Jun 12th 2021)

cross-linked the discussion of local right properness (here) with locally cartesian closed model category and with locally cartesian closed (infinity,1)-category