Can a subcategory of the category of sets be self-dual?

Question

Given that Set, the category of sets, is not self-dual, can a subcategory of Set be self-dual? If so, what are some examples?

Answer 1

Sure - consider the one-element category with a unique morphism. More generally, note that any small category is (isomorphic to) a subcategory of Set, so any small self-dual category gives an example.