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1. • CommentRowNumber1.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItexCreated a page on the set-theoretical meaning of the "class function".

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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 3rd 2017
   • (edited Jun 3rd 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIf here in a comment edit box you type [[class function (set theory)]] then the software automatically makes it a link: _[[class function (set theory)]]_

   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)

3. • CommentRowNumber3.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItex@Urs: Thanks for pointing out.

   @Urs: Thanks for pointing out.

4. • CommentRowNumber4.
   • CommentAuthorPeter Heinig
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Peter Heinig
   Format: MarkdownItexAdded two basic references to [[class function (set theory)]]

   Added two basic references to

   class function (set theory)

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI 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.

   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.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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_.

   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.

7. • CommentRowNumber7.
   • CommentAuthorMike Shulman
   • CommentTimeJun 3rd 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI clarified even further: even when using set theory, you can avoid proper classes entirely by using universes.

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