Re: Characterizing FinSet up to equivale

Hello, the simplest characterization of FinSet known to me is as the free category with initial object and binary coproducts on one object. In the usual world existence of these types of coproducts is equivalent to finite coproducts, but restriction to nullary and binary ones avoids the need for an a priori notion of finiteness. Somehow this reminds me of Kuratowski's definition of finiteness. Greetings Reinhard