Page "Isomorphism" Paragraph 43

In category theory, Iet the category C consist of two classes, one of objects and the other of morphisms.

Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.