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.
For example, of the 26 sporadic groups, 20 are subquotients of the monster group, and are referred to as the "Happy Family", while the other 6 are pariah groups.
A quotient of a subrepresentation of a representation (of, say, a group) might be called a subquotient representation; e.g., Harish-Chandra's subquotient theorem.
In constructive set theory, where the law of excluded middle does not necessarily hold, one can consider the relation 'subquotient of' as replacing the usual order relation(s) on cardinals. When one has the law of the excluded middle, then a subquotient
Transitive relation
The relation »is subquotient of« is transitive.
Let
is a homomorphism.
If
In other words: If