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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2016
    • (edited Mar 10th 2016)

    I have split off an entry classical model structure on simplicial sets from “model structure on simplicial set”. This entry should eventually contain detailed, self-contained and polished discussion of the definition, verification and key properties of the standard Kan-Quillen model structure.

    So far I have inserted fair bit of background material regarding (minimal) fibrations and geometric realizations, essentially the material in chapter 1 of Goerss-Jardine. A bunch of little proofs are spelled out, but not yet the more laborious ones. Discussion of the verification of the axioms is not yet in the entry, but the key parts of the Quillen equivalence to Top QuillenTop_{Quillen} are (modulo relying on previous lemmas that don’t have proofs spelled out yet).

    The somewhat random list of properties of sSet QuillensSet_{Quillen} that used to be sitting at “model structure on simplicial sets” I have copied over to a section “Basic properties”, just for completenes, but this now needs re-organization to give decent logical flow.

    For the moment I have to leave it at that, need to take care of something else now for a little bit.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 18th 2021

    added precise relevant section number and also full publication data for

    and added links to the electronic version of

    diff, v18, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 18th 2021

    Just so you know, the “more notes pdf” link is broken.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2021
    • (edited Mar 19th 2021)

    So I cleaned up this mess and have hosted the files now on the nLab server:

    It looks like at CRM in 2008 they were lacking somebody with a little familiarity with the internet: The authors don’t date their pdf-s and don’t cite the event they are contributions to; while the organizers either don’t host the documents, or where they do, don’t ensure that the hosting is stable.

    diff, v19, current

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 19th 2021

    Thanks! I had no idea where to start on that one.

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 19th 2021


    Constructive proofs can be found in

    diff, v20, current