# Endomorphism

A morphism `f: A → A`, that is, a morphism with identical source and target objects, is an **endomorphism** of object `A`.

An endomorphism that is also an isomorphism, is an automorphism.

A _split endomorphism_ is an _idempotent endomorphism_ `f` if `f` admits a decomposition `f = h ∘ g` with `g ∘ h = id`.

In particular, _the Karoubi envelope_ of a category splits every idempotent morphism.
