definition. isomorphism, endomorphism, automorphism [ca-0015]
Isomorphism \(A \cong B\) is a bijective homomorphism \(\phi : A \to B\)
(it follows that \(\phi ^{-1} : B \to A\) is also a homomorphism).
Endomorphism is a homomorphism from an object to itself, denoted \(\operatorname {End}(A)\).
Automorphism is an endomorphism which is also an isomorphism, denoted \(\operatorname {Aut}(A)\).