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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2023

    for completeness

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2023
    • (edited Jun 1st 2023)

    added this pointer:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2023

    added also pointer to

    (who does finally switch terminology from “simplicial groupoid” to “groupoid enriched over simplicial sets” but still does not state the definition of enriched groupoids)

    together with more comments on the history of the notion.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeJun 1st 2023

    Presumably the assumption that VV be a cosmos can be relaxed to simply asking for VV to be a cartesian monoidal category?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2023

    how about formulating it this way:

    …a cartesian monoidal category (serving as an cosmos for enrichment)…

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 1st 2023

    I think varkor is suggesting that the cosmos (or cartesian cosmos) assumptions are rather more than what is needed. In that case, I wouldn’t say “cosmos for enrichment”, but “base for enrichment” or something similar. Not sure we have a page that accommodates that extra generality, but if not, I think we should.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2023
    • (edited Jun 1st 2023)

    I know, that’s why I suggested the reformulation “serving as…”.

    Now base of enrichment is redirecting to cosmos. Feel invited to split it off as a separate entry.

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeJun 1st 2023

    Fixed a typo. id Yid_Y should have benn id Xid_X.

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 2nd 2023

    added the example of strict 2-groupoids (here)

    diff, v10, current