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nLab > Latest Changes: canonical model structure on groupoids

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2023
    • (edited Oct 31st 2023)

    I have boosted the bibitems and clarified who did what (Anderson just states the structure, without proof. Bousfield just cites Anderson. Typing up the actual proof is due to Strickland.)

    diff, v12, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 31st 2023
    • (edited Oct 31st 2023)

    Added pointer that the model structure on groupoids is a cartesian monoidal model category:

    (The theorem there is stated there for the groupoidal localization of the model structure on CatCat, instead, but it immediately applies to the model structure on groupoids, too.)

    diff, v13, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 1st 2023

    Added cartesian monoidal model structure to the existence statement (here) and added details on which references states/proves which part of the proposition.

    diff, v14, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 1st 2023

    added the remark that GrpdGrpd is locally presentable, so that Grpd canGrpd_{can} is combinatorial.

    diff, v16, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 1st 2023

    added pointer to:

    diff, v17, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2023
    • (edited Nov 5th 2023)

    Using the cartesian monoidal model structure on GrpdGrpd, one can give the “infinity-local systems” over homotopy 1-types a monoidal model category structure with respect to the external tensor product of parameterized chain complexes. This satisfies the monoid axiom for monoid objects parameterized over the point, and hence gives rise to model structures on categories of local systems of dg-modules — albeit only parameterized over 1-types.

    This is now discussed in a new section 3.4 of the version2 pdf linked to at: Entanglement of Sections.

1 to 6 of 6

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