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  1. starting page on \mathbb{Z}-functors

    Anonymouse

    v1, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTime5 days ago

    It seems, some obscure terminology.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTime3 days ago
    • (edited 3 days ago)

    Yeah, it’s not particularly convincing terminology. Also, it clashes with the terminology of Z-categories.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTime3 days ago

    Moreover, one wonders whether small (pre)sheaves, rather than all presheaves, might give the better concept, without running into size issues.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTime2 days ago

    I had a vague memory of this and I checked now, the terminology originates from Demazure-Gabriel famous functorial treatise on algebraic geometry and algebraic groups. They work with universes so the smallness is accounted for appropriately.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTime2 days ago

    I meant small in the sense of being a small colimit of representables, not valued in small sets, in case that wasn’t clear. I see from this MathOverflow answer D&G are imposing the constraint that a Z-functor is only defined on a subcategory of “very small” rings, relative to the smaller of a pair of universes.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime1 day ago

    So I have added pointer to Demazure & Gabriel, and at the top a disambiguation warning regarding functors between Z-categories.

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTime1 day ago

    6 Oh, right, I forgot about that.