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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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Functor category's objects fail to be a class?
This can be circumvented (to some degree) if we use Grothendieck universes instead of classes. Roughly speaking, a set $\mathcal U$ is a universe if it's closed under all the operations we use in ZF. …