##  [Endomorphism](/endomorphism) 

  ##  [Endomorphism](https://mathlogic.quantumdictionary.io/endomorphism-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Endomorphism](https://puremath.quantumdictionary.io/endomorphism-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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

 

 

 

 

 





 

 



 ##  [Endomorphism](https://algebra.quantumdictionary.io/endomorphism-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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