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.
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