Endomorphism is such morphism (morphism is another term for homomorphism) whose source and destination are the same object.

That is a morphism is endomorphism, when where is some object (e.g. may be an abstract algebra). Then one can say, the object of endomorphism is .

In the most general case endomorphisms are encountered in category theory. As a special case of this endomorphisms are also encountered in abstract algebra.

A morphism which is both an endomorphism and an isomorphism is called automorphism.

The sets of endomorphisms and automorphisms for an object of a category are often denoted correspondingly as and or sometimes as and .

Endomorphisms also can be considered as objects of category of intermorphisms and (if the set of morphisms of our category is preordered) also of category of pseudomorphisms.