a quotient category is a category obtained from another category by identifying sets of morphisms. Formally, it is a quotient object in the category of...

(mathematics) Quotient category Quotient graph Integer division Quotient module Quotient object Quotient of a formal language, also left and right quotient Quotient...

In mathematics, the quotient (also called Serre quotient or Gabriel quotient) of an abelian category A {\displaystyle {\mathcal {A}}} by a Serre subcategory...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup. In category theory, quotient groups...

quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories. An equivalence relation on...

mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of...

kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of...

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked...

terms of categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer science also rely on category theory...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

morphisms. This is a quotient category of Top. One can likewise form the pointed homotopy category hTop•. Top contains the important category Haus of Hausdorff...

functors from A to another abelian category. C is a localizing subcategory if it is a Serre subcategory such that the quotient functor Q : A → A / C {\displaystyle...

In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type...

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...

In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

Applied category theory Category of sets Concrete category Category of vector spaces Category of graded vector spaces Category of chain complexes Category of...

An intelligence quotient (IQ) is a total score derived from a set of standardised tests or subtests designed to assess human intelligence. The abbreviation...

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...

In category theory, a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle...

algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

in the category of commutative R-algebras is the tensor product. In the category of (noncommutative) R-algebras, the coproduct is a quotient of the tensor...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

space Quotient (universal algebra) Quotient object in a category Quotient category Quotient of a formal language Quotient type Intelligence quotient, a psychological...

from the category of abelian groups to category of groups. It has a left adjoint called abelianization which assigns to every group G the quotient group...

quasi-isomorphisms. Given an abelian category A and a Serre subcategory B, one can define the quotient category A/B, which is an abelian category equipped with an exact...

theory and the cokernel is the quotient map onto the ordinary cokernel from group theory. Other common examples: The category of (left) modules over a ring...