Definition 0.1
A morphism f : A → B in a category C is an isomorphism when there exists an inverse morphism
of f in C, denoted by f−1 : B → A, such that f ∘ f−1 = id
A = 1A : A → A.
One also writes: A
B, expressing the fact that the object A is isomorphic with object B under
the isomorphism f.
Note also that an isomorphism is both a monomorphism and an epimorphism; moreover, an
isomorphism is both a section and a retraction. However, an isomorphism is not the same as an
equivalence relation.
