[tupshin]

I've found the best layman's grounding for Category theory's relationship to axioms to be in Bartosz's post here:

https://www.quora.com/Are-there-any-axioms-for-category-theo...

[red_trumpet]

That's a nice post, and it actually reinforces my thoughts: You already need a foundational theory before coming to category theory.

[sylware]

Well... then set theory with core logic still THE foundation then.