subquotient
Sign in to saveAlso known as section
In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject. Subquotients are particularly important in abelian categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory.
Wikidata facts
- Subclass of
- quotient algebra
Show 2 more facts
- facet of
- group theory
- maintained by WikiProject
- WikiProject Mathematics
via Wikidata · CC0
~4 min read
Encyclopedic overview
6 sectionsContents
- Example
- Order relation
- Proof of transitivity for groups
- Relation to cardinal order
- See also
- References
In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject. Subquotients are particularly important in abelian categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory.
So in the algebraic structure of groups, H is a subquotient of G if there exists a subgroup G' of G and a normal subgroup G'' of G' so that H is isomorphic to G'/G.
Excerpted from Wikipedia’s “subquotient” article, available under the CC BY-SA 4.0 licence.