e/Adjoint functors

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has glosseng: In mathematics, adjoint functors are pairs of functors which stand in a particular relationship with one another, called an adjunction. The relationship of adjunction is ubiquitous in mathematics, as it rigorously reflects the intuitive notions of optimization and efficiency. It is studied in generality by the branch of mathematics known as category theory, which helps to minimize the repetition of the same logical details separately in every subject.
lexicalizationeng: adjoint functors
subclass of(noun) that which is perceived or known or inferred to have its own distinct existence (living or nonliving)
entity
has instancee/Apply
has instancee/Distributive law between monads
has instancee/Equivalence of categories
has instancee/Isomorphism of categories
has instancee/Kan extension
has instancee/Kleisli category
has instancee/Monad (category theory)
has instancee/Monoidal adjunction
has instancee/Reflective subcategory
has instancee/Strong monad
Meaning
German
has glossdeu: Adjungiert heißen zwei F: C → D, G: D → C zwischen zwei C und D, die gewissermaßen ein Ersatz für eine fehlende Äquivalenz von Kategorien sind.
lexicalizationdeu: Adjunktion
French
lexicalizationfra: adjoint
Korean
has glosskor: 수학에서 수반 펑터(adjoint functor)는 두 개의 펑터가 서로간에 가질 수 있는 일종의 밀접한 관계이다. 이는 수학의 많은 분야에서 널리 나타나는 관계이며, 범주론의 연구 대상이다.
lexicalizationkor: 수반 펑터
Russian
has glossrus: Сопряжённые функторы в математике и в частности в теорий категорий — это пара функторов, состоящих в определённом соотношении между собой. Сопряжённые функторы часто встречаются в разных областях математики.
lexicalizationrus: Сопряженные функторы
lexicalizationrus: Сопряжённые функторы
Castilian
has glossspa: La existencia de muchos pares de funtores adjuntos es una observación importante de la rama de la matemática conocida como teoría de categorías. (La teoría de categorías continúa en cierta forma la visión estructuralista en matemática; ver también estructura algebraica, estructura (teoría de las categorías).). Los funtores adjuntos se pueden considerar desde varios puntos de vista. Este artículo comienza con unas cuantas secciones introductorias que consideran algunos de ellos.
lexicalizationspa: funtores adjuntos
Chinese
has glosszho: 在範疇論中,函子 F, G 若滿足 \mathrmHom}(F(-),-) = \mathrmHom}(-,G(-)) ,則稱之為一對伴隨函子,其中 G 稱為 F 的右伴隨函子,而 F 是 G 的左伴隨函子。伴隨函子在範疇論中是個極基本而有用的概念。
lexicalizationzho: 伴隨函子
Media
media:imgAdjointFunctorSymmetry.png
media:imgAdjointFunctors-01.png
media:imgAdjointFunctorsHomSets.png

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