608: Quotient Category

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definition of quotient category

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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

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Starting Context

• The reader knows a definition of congruence on category.

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Target Context

• The reader will have a definition of quotient category.

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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:
$C$: $\in \{\text{ the categories }\}$
$\sim$: $\in \{\text{ the congruences on }C\}$
$\ast C^{\prime }$: $\in \{\text{ the categories }\}$
//

Conditions:
$Obj(C^{\prime })=Obj(C)$.
$\wedge$
$Mor(C^{\prime })=Mor(C)/\sim$.
//

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2: Natural Language Description

For any category, $C$, and any congruence on $C$, $\sim$, the category, $C^{\prime }$, such that $Obj(C^{\prime })=Obj(C)$ and $Mor(C^{\prime })=Mor(C)/\sim$

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References

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