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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMay 3rd 2021

    When we say

    A category CC is cofinally small if there is a small category C 0C_0 and a cofinal functor C 0CC_0 \to C.

    does “cofinal functor” mean “final functor” or “co-(final functor)” i.e. “initial functor”?

    The only links to this page I can find are from calculus of fractions, where my guess would be that what’s meant is “initial functor”, and from ind-object, where my guess would be that what’s meant is “final functor”. So I don’t know.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeMay 3rd 2021
    • (edited May 3rd 2021)

    I think that ’final functor’ is the almost universal meaning in the literature; in fact, whilst I’m writing this quickly, I would have thought this is also what is meant at calculus of fractions?

    What a terribly confusing piece of terminology!

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 3rd 2021
    • (edited May 3rd 2021)

    This was discussed here: https://nforum.ncatlab.org/discussion/9054/final-functor/.

    Apparently, Borceux’s Handbook of Categorical Algebra and Lurie’s Higher Topos Theory use “cofinal functor” for the concept that all other books call “final functor”.

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