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nLab > Latest Changes: model structure on simplicial presheaves

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  1.  
    • 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:

    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.)

    • 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.

    diff, v130, current

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeMar 29th 2019

    Fixed some ?ech which should have been Čech.

    diff, v134, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2020

    I have added publication data to

    diff, v137, current

    • 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

    diff, v142, current

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