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    • CommentRowNumber1.
    • CommentAuthorPeter Heinig
    • CommentTimeJun 3rd 2017

    Created a page on the set-theoretical meaning of the “class function”.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 3rd 2017
    • (edited Jun 3rd 2017)

    If here in a comment edit box you type

      [[class function (set theory)]]
    

    then the software automatically makes it a link:

    class function (set theory)

    • CommentRowNumber3.
    • CommentAuthorPeter Heinig
    • CommentTimeJun 3rd 2017

    @Urs: Thanks for pointing out.

    • CommentRowNumber4.
    • CommentAuthorPeter Heinig
    • CommentTimeJun 3rd 2017

    Added two basic references to

    class function (set theory)

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 3rd 2017

    I tweaked a phrase to read, “Class functions are an important concept when formalizing category theory on set-theoretic foundations…”. The point is that there can be many ways of laying formal foundations for category theory: Mac Lane took recourse in a set-theoretic framework back in the early 1970’s, but today there are various options.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 3rd 2017

    I suggest to add an Idea-section that provides some context, maybe such as the following:

    Recall that in set theory a function ff from a set S 1S_1 to a set S 2S_2 may be encoded in terms of a relation on the Cartesian product S 1×S 2S_1 \times S_2 of the two sets, namely the subset RS 1×S 2 R \subset S^1 \times S^2 with R={(x,y)|y=f(x)}R = \{ (x,y) \vert y = f(x)\}.

    This concept has an evident generalization to the case where S 1S_1 and S 2S_2 are allowed to be proper classes. In this case one speaks of class functions.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJun 3rd 2017

    I clarified even further: even when using set theory, you can avoid proper classes entirely by using universes.

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