A set being a member if itself (or not) is the source of the famous paradox that destroyed the naive set theory %)

In practice, you usually need either a definite sum.type (int | str | null), or the all-encompassing type, like Any. I think both cases should be adequately representable in a categorial language — am I wrong?

You may need to represent a sum type that includes Any (or a similar type) if you.allow type-based signature overloads for functions. I wonder if this may represent any obstacle to a caregorial approach.