A definition of %structure kind name% endomorphism
Topics
About: structure
The table of contents of this article
Starting Context
- The reader knows a definition of structure.
- The reader knows a definition of morphism.
Target Context
- The reader will have a definition of %structure kind name% endomorphism.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For any structure, \(S\), any morphism, \(f: S \to S\)
2: Note
Often called just "endomorphism", any morphism is never just a "endomorphism", but a group endomorphism, a vectors space endomorphism, etc., depending on what kind of structure the morphism is regarded to be of, which is the reason why the title of this article is "%structure kind name% endomorphism" with "%structure kind name%" as a place holder.
For example, when the domain and the codomain, \(S\), is a vectors space (which means that that is automatically also a group with addition as the group operation), a map may be a group endomorphism, but not a vectors space endomorphism.
