What is "endomorphism"

n. 1 (context geology English) The assimilation of surrounding rock by an intrusive igneous rock 2 (context mathematics English) A homomorphism that maps a system to itself

In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself. For example, an endomorphism of a vector space, is a linear map, , and an endomorphism of a group, , is a group homomorphism . In general, we can talk about endomorphisms in any category. In the category of sets, endomorphisms are functions from a set S to itself.

In any category, the composition of any two endomorphisms of is again an endomorphism of . It follows that the set of all endomorphisms of forms a monoid, denoted (or to emphasize the category ).