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Re:Topology, a Categorical Approach by ghancock on Monday November 14, 2022 @09:17PM (#33604440)
> On the other hand, I've not seen a rigorous set of axioms for category theory that didn't presuppose a notion of set or category or "collection".

I never worked through the details, and I'm not a category theory partisan, but I think that's what this is: https://ncatlab.org/nlab/show/fully%20formal%20ETCS

Re:Topology, a Categorical Approach by Twisol on Monday November 14, 2022 @11:04PM (#33605126)
Yes, this is essentially what I'm getting at in my cousin comment -- although the nlab is typically rather impenetrable to non-specialists.