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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

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

This concept has an evident generalization to the case where $S_1$ and $S_2$ 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.