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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
6
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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. …