Enriched category
In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category. It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., that of being a vector space of morphisms, or a topological space of morphisms. In an enriched category, the set of morphisms (the hom-set) associated with every pair of objects is replaced by an object in some fixed monoidal category of "hom-objects". In order to emulate the (associative) composition of morphisms in an ordinary category, the hom-category must have a means of composing hom-objects in an associative manner: that is, there must be a binary operation on objects gi
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2-functorAB5 categoryAbelian categoryAdditive categoryArrow (computer science)Bousfield localizationCategory (mathematics)Category enrichedCategory theoryChu spaceCosmos (category theory)Day convolutionEnriched categoriesEnriched category theoryEnriched functorEnrichmentEqualiser (mathematics)Glossary of category theoryHigher-dimensional algebraHigher category theoryInternal categoryIsbell conjugacyMax KellyMeasuring coalgebraMetric spaceMonoidal categoryOutline of category theoryPosetal categoryPre-abelian categoryPreadditive categoryPreorderQuantaloidSimplicially enriched categoryStrict 2-categoryTimeline of category theory and related mathematicsTopological categoryV-category
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Enriched category
In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category. It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., that of being a vector space of morphisms, or a topological space of morphisms. In an enriched category, the set of morphisms (the hom-set) associated with every pair of objects is replaced by an object in some fixed monoidal category of "hom-objects". In order to emulate the (associative) composition of morphisms in an ordinary category, the hom-category must have a means of composing hom-objects in an associative manner: that is, there must be a binary operation on objects gi
has abstract
In category theory, a branch o ...... to generally as V-categories.
@en
In de categorietheorie, een ab ...... een zich goedgedragende wijze.
@nl
In der Kategorientheorie ist d ...... r Kategorien verwendet werden.
@de
Une catégorie enrichie sur une ...... ucture, sont des éléments de .
@fr
Обогащённая категория в теории ...... егорией над , или -категорией.
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数学の一分野、圏論における豊穣圏(ほうじょうけん、英: en ...... っていたから、豊饒圏のことも一般に V-圏と呼ぶこともある。
@ja
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enriched+category
@en
title
Enriched category
@en
wikiPageUsesTemplate
comment
In category theory, a branch o ...... binary operation on objects gi
@en
In de categorietheorie, een ab ...... een zich goedgedragende wijze.
@nl
In der Kategorientheorie ist d ...... erwendet werden können sollen.
@de
Une catégorie enrichie sur une ...... ucture, sont des éléments de .
@fr
Обогащённая категория в теории ...... уктуру моноидальной категории.
@ru
数学の一分野、圏論における豊穣圏(ほうじょうけん、英: en ...... のである。そのような構造として以下のようなものが挙げられる:
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label
Angereicherte Kategorie
@de
Catégorie enrichie
@fr
Enriched category
@en
Verrijkte categorie
@nl
Обогащённая категория
@ru
豊穣圏
@ja
풍성한 범주
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