82: Morphism

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definition of morphism

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Topics

About: category

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description
• 3: Note

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Starting Context

• Nothing.

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Target Context

• The reader will have a definition of morphism.

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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: Structured Description

Here is the rules of Structured Description.

Entities:
$O_1$: $\in \{\text{ the objects }\}$
$O_2$: $\in \{\text{ the objects }\}$
$\ast m$: $:O_1\to O_2$, $\in \{\text{ the arrows from }{O}_1\text{ to }{O}_2\}$


Conditions:
//

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2: Natural Language Description

For any ordered pair of objects, $(O_1,O_2)$, any arrow, $m:O_1\to O_2$

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3: Note

"What is "object" or "arrow"?" is a natural question, but 'object' is any entity and 'arrow' is anything that connects any 2 objects with any direction.

Typically, an object is a set, and a morphism is a map, but they are generalized to be not necessarily so.

Usually, a morphism is called so as an ingredient of a category.

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References

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