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...

morphism Dual (category theory) Groupoid Image (category theory) Coimage Commutative diagram Cartesian morphism Slice category Isomorphism of categories Natural...

In category theory, a branch of mathematics, the opposite category or dual category C op {\displaystyle C^{\text{op}}} of a given category C {\displaystyle...

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 abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...

Autonomous category Convex body and polar body. Dual abelian variety Dual basis Dual (category theory) Dual code Duality (electrical engineering) Duality (optimization)...

order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order...

category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...

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...

the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...

In category theory, a branch of mathematics, a section is a right inverse of some morphism. Dually, a retraction is a left inverse of some morphism. In...

In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...

mirror one another Dual (category theory), a formalization of mathematical duality see more cases in Category:Duality theories Dual number, a number system...

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

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 cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances...

object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that...

Look up duality in Wiktionary, the free dictionary. Duality may refer to: Duality (mathematics), a mathematical concept Dual (category theory), a formalization...

several decades in string theory was the discovery of certain 'dualities'—mathematical transformations that identify one physical theory with another. Physicists...

In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is...

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 category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...

In category theory and related fields of mathematics, a refinement is a construction that generalizes the operations of "interior enrichment", like bornologification...

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 psychology, a dual process theory provides an account of how thought can arise in two different ways, or as a result of two different processes. Often...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of...

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal...

In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in...

Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras...