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Endomorphism
In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself. For example, an endomorphism of a vector space ''V'' is a linear map , and an endomorphism of a group ''G'' 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 ''X'' is again an endomorphism of ''X''. It follows that the set of all endomorphisms of ''X'' forms a monoid, denoted End(''X'') (or End''C''(''X'') to emphasize the category ''C'').
==Automorphisms==
(詳細はinvertible endomorphism of ''X'' is called an automorphism. The set of all automorphisms is a subset of End(''X'') with a group structure, called the automorphism group of ''X'' and denoted Aut(''X''). In the following diagram, the arrows denote implication:
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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