411: %Structure Kind Name% Endomorphism

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definition of %structure kind name% endomorphism

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Topics

About: structure

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition
• 2: Note

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Starting Context

• The reader knows a definition of structure.
• The reader knows a definition of morphism.

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Target Context

• The reader will have a definition of %structure kind name% endomorphism.

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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.

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Main Body

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1: Definition

For any structure, $S$, any morphism, $f:S\to S$

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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.

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References

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