##  [Non-Hopfian Object](/non-hopfian-object) 

  ##  [Non-Hopfian Object](https://algebra.quantumdictionary.io/non-hopfian-object-0) 

  

 [![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

An object in a category (commonly a module, group, or algebraic structure) admitting a surjective endomorphism that is not an isomorphism; equivalently, surjectivity of an endomorphism does not imply invertibility for that object.