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# endomorphism

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

That is a morphism $f$ is *endomorphism*, when $\mathrm{Src}f=\mathrm{Dst}f=A$ where $A$ is some object (e.g. $A$ may be an abstract algebra). Then one can say, the object of endomorphism $f$ is $A$.

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 $A$ of a category are often denoted correspondingly as $\mathrm{End}(A)$ and $\mathrm{Aut}(A)$ or sometimes as $\mathrm{end}(A)$ and $\mathrm{aut}(A)$.

*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.

## Mathematics Subject Classification

18A20*no label found*18A05

*no label found*

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