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Is it an isomorphism?
Suppose that someone tells you that their category \(C \) has two objects \(c,d \) and two non-identity morphisms, \(f : c \to d \) and \(g : d \to c \), but no other morphisms. Does \(f \) have to be the inverse of \(g \), i.e. is it forced by the category axioms that \( g◦f = id_c \) and \(f◦g= id_d \)?