I want to write about something simple that connects category and set theory. I was told that in $\boldsymbol{\operatorname{Set}}$, the axiom of choice is equivalent to every epimorphism being split, so it's also possible to ask which categories satisfy the axiom of choice. However, I don't know any literature on this, so my point here is if anyone knows any (beginner) books on something like this that would connect those two theories.
2026-05-16 06:27:33.1778912853
Literature on category theory/set theory
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You might be interested in Rosebrugh-Lawvere's book Sets for Mathematics, introducing set theory in a categorical fashion, aimed towards undergraduate students. Also most books on topos theory have at least some chapters on the connection to set theory, MacLane-Moerdijk's Sheaves in Geometry and Logic §VI and Johnstone's Topos Theory come to mind. These sources are a bit more advanced though.