What is the relationship, if any, between set-theoretically defined functions and morphisms (or the arrow thingies) from category theory?
2026-03-27 09:37:39.1774604259
Are set-theoretically defined functions and category-theoretic morphisms equivalent notions?
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I don't think there is one (and to many, that's the point of "category"). The one arguable link is that the definition of a category requires set-theoretic functions in order to define composition, usually as a map $$ \mathrm{Hom}(A,B) \times \mathrm{Hom}(B,C) \to \mathrm{Hom}(A,C). $$