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nLab > Latest Changes: Changed something at hom-functor

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    • CommentRowNumber1.
    • CommentAuthorOC
    • CommentTimeFeb 8th 2016
    Greetings, newbie here (which is why I haven't used tags, just haven't figured out how). I'm also new to category theory, but representable functors being described as "functors equivalent to hom-functors" in the hom-functor article and as "functors naturally isomorphic to hom-functors" in the representable functor article is confusing to say the least. As some other sources say it's naturally isomorphic rather than equivalent, I changed the hom-functor article, and added a link for good measure. Again, I'm completely inexperienced at both category theory and nLab, so sorry if I messed anything up!
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2016
    • (edited Feb 8th 2016)

    Thanks, that’s okay.

    There is this story that as one generalizes to higher category theory, then what generalizes “isomorphism” is equivalence. So “equivalence” in a way is a more robust term. For instance the concept of representable functors generalizes verbatim to all of higher category theory if instead of “natural isomorphism” here one says “natural equivalence”.

    But since the entry didn’t make that clear, and if you say it was in fact confusing, then it’s good that you changed it. Thanks.

  3. Welcome! I think that both “naturally isomorphic” and “equivalent” are correct, but it’s good that you’ve changed it so that we’re consistent.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 8th 2016

    FWIW, the seminar paper of category theory was titled General theory of natural equivalences…

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 8th 2016

    seminar -> seminal

1 to 5 of 5

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