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nLab > Latest Changes: locally graded category

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  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeJun 5th 2023

    Create a stub for this concept.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeJun 5th 2023

    Mention locally indexed categories and a connection to simplicially enriched categories.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2023

    I have touched wording, formatting and hyperlinking and completed the publication data for the articles by Wood and Riehl.

    Mainly I took the liberty of adjusting the wording of this paragraph:

    This gives an abstract proof of the fact that simplicially enriched categories can be viewed as functors into the category of small categories and identity-on-objects functors (see Proposition 1.2.3 of Riehl).

    to the following:

    For example, with Levy (2019), slide 21 this gives an abstract proof of the standard fact that simplicially enriched categories can be viewed as those simplicial objects in Cat which take value in identity-on-objects functors (e.g. Riehl (2023), Prop. 1.2.3).

    Here I think it’s Levy’s slide 21 that you mean to be referring to. But that slide is most brief, this would deserve a more detailed reference.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeJun 6th 2023

    You’re right, the remark probably comes across as a little cryptic at the moment. I’ll try to find time to expand upon it later.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2023

    All right, thanks.

    A good abstract discussion of the relation between sSetsSet-enriched categories and simplcial objects in categories would be worthwhile to point to also from sSet-enriched category and enriched groupoid, etc.:

    The reflection of this equivalence in the literature is somewhat curious (as reflected eg. in the references here): Everybody must feel it’s too trivial to dwell on (also the proposition by Riehl that you point to doesn’t really say more than that) and nobody takes the extra step of categorical algebra to “show that it’s trivially trivial”.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeDec 15th 2023

    Spelled out the definition of a locally graded category.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeJul 25th 2024

    Mentioned skew-proactegories.

    diff, v8, current

1 to 7 of 7

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