definition of quotient category
Topics
About: category
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of congruence on category.
Target Context
- The reader will have a definition of quotient category.
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.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( C\): \(\in \{\text{ the categories }\}\)
\( \sim\): \(\in \{\text{ the congruences on } C\}\)
\(*C'\): \(\in \{\text{ the categories }\}\)
//
Conditions:
\(Obj (C') = Obj (C)\).
\(\land\)
\(Mor (C') = Mor (C) / \sim\).
//
2: Natural Language Description
For any category, \(C\), and any congruence on \(C\), \(\sim\), the category, \(C'\), such that \(Obj (C') = Obj (C)\) and \(Mor (C') = Mor (C) / \sim\)
