In mathematics, the Stone functor is a functor S: Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras...

relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in...

is openPages displaying short descriptions of redirect targets Stone functor – Functor in category theory Profinite group – Topological group that is...

Boolean algebras. Stone was the son of Harlan Fiske Stone, who was the Chief Justice of the United States in 1941–1946. Marshall Stone's family expected...

is equivalent to finding a functor from Frm to Top which is adjoint to Ω. The goal of this section is to define a functor pt from Frm to Top that in a...

equivalence of categories consists of a functor between the involved categories, which is required to have an "inverse" functor. However, in contrast to the situation...

right Kan extension of the identity functor of the category CHaus of compact Hausdorff spaces along the inclusion functor of CHaus into the category Top of...

contravariant functor acts as a covariant functor from the opposite category Cop to D. A natural transformation is a relation between two functors. Functors often...

Technically, a universal property is defined in terms of categories and functors by means of a universal morphism (see § Formal definition, below). Universal...

that is equipped with a faithful functor to Set, the category of sets. Let C be a concrete category with a faithful functor U : C → Set. Let X be a set (that...

topological space X is replaced by the functor that takes a profinite set S to the set of continuous maps from S to X. Stone–Čech compactification#Construction...

The third condition is equivalent to the requirement that the functor – ×Y (i.e. the functor from C to C that maps objects X to X ×Y and morphisms φ to φ × idY)...

ind-completed category, denoted Ind(C), are known as direct systems, they are functors from a small filtered category I to C. The dual concept is the pro-completion...

duality can be recovered via a functor that replaces the field of sets with the Boolean space it generates. Via a functor that instead replaces the pre-order...

contravariant power set functor, P: Set → Set and P: Set op → Set. The covariant functor is defined more simply as the functor which sends a set S to P(S)...

category where the functor X ↦ X ⊗ A {\displaystyle X\mapsto X\otimes A} has a right adjoint, which is called the "internal Hom-functor" X ↦ H o m C ( A...

Dual (category theory) Duality (mathematics) Adjoint functor Contravariant functor Opposite functor "Is there an introduction to probability theory from...

contravariant functor from the category of commutative rings to the category of locally ringed spaces. In fact it is the universal such functor, and hence...

duality, Hartshorne (Algebraic Geometry) uses the Ext functor of sheaves; this is a kind of stepping stone to the derived category. The classical statement...

subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint.: 91  This adjoint is sometimes called a...

fundamental construction associating a monad to a wide class of functors. The codensity monad of a functor G : D → C {\displaystyle G:D\to C} is defined to be the...

Hom functor and the tensor product functor might not lift to an exact sequence; this leads to the definition of the Ext functor and the Tor functor. In...

limits and exact sequences. For this reason, regular functors are sometimes called exact functors. Functors that preserve finite limits are often said to be...

Standard Library. It provides four components called algorithms, containers, functors, and iterators. The STL provides a set of common classes for C++, such...

denotes the quotient space. The Alexandroff extension can be viewed as a functor from the category of topological spaces with proper continuous maps as...

theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. This functor assigns to each space its dual space, and the...

Ph.D. at Harvard University in 1942 under the direction of Marshall H. Stone. He joined the Harvard University Mathematics Department in 1943, was appointed...

homological methods, such as the Ext functor. This functor is the derived functor of the functor HomR(M, −). The latter functor is exact if M is projective, but...

functor Ω {\displaystyle \Omega } from the category of topological spaces and continuous maps to the category of locales. If we restrict this functor...

and a monoidal functor to its underlying morphism of signatures, i.e. it forgets the identity, composition and tensor. The free functor C − : M o n S i...