Subquotient

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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.

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