_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 \\)?

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 \\)?