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  1. Section “Necessity of naturality” sounded like there is nothing interesting going on if we look at the unnatural isomorphism of hom-sets. But this isn’t the case, already in the 60s a graph-theoretical and purely categorical facts of this form have been established. I’m adding the two earliest references.

    Tomas Jakl

    diff, v72, current

    • CommentRowNumber102.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2021
    • (edited Jun 18th 2021)

    The entry fell short of really citing the following in full, so I have added it now:

    diff, v73, current

  2. adding text from HoTT wiki.


    diff, v76, current

    • CommentRowNumber104.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    This edit needs analogous adjustments to those pointed out in another thread here.

    I am out of energy for the moment. Please look into it. Generally, please try to keep in mind that nLab entries need to retain a minimum of logical consistency as you drop material into them that is copied from elsewhere.

    diff, v77, current

    • CommentRowNumber105.
    • CommentAuthorkrinsman
    • CommentTimeMar 31st 2024
    Would it be OK to edit the page to use consistent notation for Hom sets throughout? (Or at least for the Hom sets of the generic category "C"?)

    At one point in the article they're denoted Hom_C (...), but elsewhere they're denoted C(...).

    Of course changing it from the latter would require then changing the notation for the Hom-sets of other categories mentioned, e.g. Set(...) to Hom_Set (...).

    I'm willing to scan through the article and make the change to either convention, it's just unclear to me which convention should be preferred.

    Having two distinct conventions (or no notice / warning of the switch between them) seems like it would be very confusing to someone using this article as an introduction. (And is honestly somewhat jarring to me even as someone already moderately familiar with the topic.)
    • CommentRowNumber106.
    • CommentAuthorUrs
    • CommentTimeMar 31st 2024

    This happens when different authors edit different bits at different times.

    If you have the energy to harmonize the notation, it would be a welcome service to the community.

    The notation C(...)C(...) tends to indicate that the construction also works in the enriched context, while the notation Hom C(...)Hom_C(...) makes clear that one does insist to mean plain Hom-sets.

    So I suppose that C(...)C(...) is a good choice for this page.

  3. Rename parameter of the inverse of the Yoneda map to clarify that the “functional” component of (X(c)\to (C(-,c)\to X(d)) comes from the (C(-,c)) component, not the (X(c)) component.

    This also keeps notation more consistent with the forward direction.

    Dov Mostovicz

    diff, v82, current