I realized this while reading about higher categories. What exceeds basic set theory, namely ZFC and cardinals/ordinals formalism and beyond was always intimidating to me at first glance. But seeing the categorical constructions, and namely the formalism of Grothendieck universes and how Grothendieck predicted the n-stacks, made me realize how underrated axiomatic set theory is.
Gödel's second incompleteness theorem, that seems counter-intuitive at first, provided the actual limits of classical ZFC model when it comes to defining categorical objects without stumbling on logical paradoxes. I do remember seeing something like that in the construction of condensed categories but it's my first time exploring it in depth.