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nLab > Latest Changes: model structure on simplicial abelian groups

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2021
    • (edited Jul 10th 2021)

    I thought we already long had this as an entry – but, no, it was re-directing all along to model structure on simplicial algebras. Am giving it its own entry now, but it remains telegraphic for the moment.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 10th 2021

    Added:

    In fact, much more is true: all five classes of maps in a model category (weak equivalences, (acyclic) cofibrations, and (acyclic) fibrations) are preserved and reflected by both of these equivalences. That is to say, each model structure is obtained from the other one by transferring it along the corresponding equivalence of categories.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2021
    • (edited Jul 11th 2021)

    Thanks, right. The section Dold-Kan correspondence – As a Quillen equivalence of model categories, that is pointed to, essentially says this – in stating that the DK-equivalence is Quillen in both orientations – and more. That section should be imported here and maybe be polished-up in the process, but I don’t have the energy right now.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2021

    added brief statement (here) of the monoidal model structure

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 14th 2021

1 to 5 of 5

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