Definition. Inverses and isomorphism [inverses-and-isomorphism]

If , are morphisms.

• is a left inverse of when .
• is a right inverse of when .
• is a section if it has a left inverse.
• is a retraction if it has a right inverse.
• is an isomorphism if it is both a section and a retraction. We will also introduce the notation for an isomorphism .