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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.

Jonas Linssen
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Max
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  • Be more specific. "Something" can mean a lot of things - a paper, a book, a magazine article, a student essay. What level are you, and what level is your target audience? – Thomas Andrews Jul 01 '23 at 15:00
  • You might be interested in these questions: 1 and 2 – HallaSurvivor Jul 01 '23 at 15:07
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    For example, the book "Sheaves in Geometry and Logic" has a great reframing of the famous forcing proofs of independence of the continuum hypothesis and other results from set theory. But that's a graduate-level book. – Thomas Andrews Jul 01 '23 at 15:15

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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.

Jonas Linssen
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