Let's say we have a set S, and a function f : S -> S. Now let S be endowed with a binary operation, forming a group G. Is it correct to write f : G - > G?(adsbygoogle = window.adsbygoogle || []).push({});

Up to now I have been operating on the assumption that yes, although G is not technically a set, there is little harm in being sloppy and use G to designate its underlying set, S.

However someone has recently told me that this is not correct. f : G - > G is different from f : S - > S. I was referred to category theory, of which I admittedly know nothing.

Is this true?

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# Logical distinction between sets and algebraic structures

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