Subquotient
Encyclopedia
In the mathematical
fields of category theory
and abstract algebra
, a subquotient is a quotient object of a subobject
. Subquotients are particularly important in group theory
, where they are also known as sections
, and in abelian categories.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
fields of category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
and abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
, a subquotient is a quotient object of a subobject
Subobject
In category theory, a branch of mathematics, a subobject is, roughly speaking, an object which sits inside another object in the same category. The notion is a generalization of the older concepts of subset from set theory and subgroup from group theory...
. Subquotients are particularly important in group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, where they are also known as sections
Section (group theory)
In group theory a section of a group G is a group that is, or is isomorphic to, a quotient group of a subgroup of G.- Examples :Of the 26 sporadic groups, 20 are sections of the monster group, and are referred to as the "Happy Family"....
, and in abelian categories.