Definition for "Endomorphism" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

A morphism from an object to itself: f: X → X. Unlike an automorphism, an endomorphism need not be invertible; endomorphisms are studied as algebraic operators on the object and form a monoid under composition.

- Mathematics & Logic -

Pure Mathematics Dictionary

A homomorphism from an object to itself in a given category; it preserves the defining structure but need not be invertible.

- Pure Mathematics -

Algebra Dictionary

A homomorphism from an algebraic object to itself: f: A → A that preserves the defining operations of A.