Representable functor (original) (raw)
Darstellbarkeit ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. Es beschreibt den Umstand, dass es für gewisse Konstruktionen "klassifizierende Objekte" gibt.
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| dbo:abstract | Darstellbarkeit ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. Es beschreibt den Umstand, dass es für gewisse Konstruktionen "klassifizierende Objekte" gibt. (de) On rencontre en mathématiques de nombreuses propriétés universelles. Le formalisme des catégories permet d'exprimer ces propriétés de façon très simple. (fr) In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory. (en) 범주론에서 표현 가능 함자(表現可能函子, 영어: representable functor)는 어떤 요네다 함자와 자연 동형인 함자이다. (ko) Em teoria das categorias, dada categoria , uma representação para um functor é um objeto junto a um isomorfismo natural em que denota o functor hom. Um functor representável é um functor admitindo representação. (pt) В теории категорий, представимый функтор — функтор специального типа из произвольной категории в категорию множеств. В некотором смысле, такие функторы задают представление категории в терминах множеств и функций. (ru) 可表函子是在数学中范畴论里的概念，指从任意范畴到集合范畴的一种特殊函子。这种函子将抽象的范畴表达成人们熟知的结构（即集合与函数），从而使得对集合范畴的了解可以尽可能应用到其它环境中。 从另外一个角度看，范畴的可表函子是随范畴而生的。因此，可表函子理论可以视作偏序集合理论中的上闭集合以及群论中的凱萊定理的极大的推广。 (zh) В теорії категорій, зображуваний функтор — функтор спеціального типу з довільної категорії в категорію множин. У певному сенсі, такі функтори задають опис категорії в термінах множин і функцій. (uk) |
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| rdfs:comment | Darstellbarkeit ist ein Begriff aus dem mathematischen Teilgebiet der Kategorientheorie. Es beschreibt den Umstand, dass es für gewisse Konstruktionen "klassifizierende Objekte" gibt. (de) On rencontre en mathématiques de nombreuses propriétés universelles. Le formalisme des catégories permet d'exprimer ces propriétés de façon très simple. (fr) In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory. (en) 범주론에서 표현 가능 함자(表現可能函子, 영어: representable functor)는 어떤 요네다 함자와 자연 동형인 함자이다. (ko) Em teoria das categorias, dada categoria , uma representação para um functor é um objeto junto a um isomorfismo natural em que denota o functor hom. Um functor representável é um functor admitindo representação. (pt) В теории категорий, представимый функтор — функтор специального типа из произвольной категории в категорию множеств. В некотором смысле, такие функторы задают представление категории в терминах множеств и функций. (ru) 可表函子是在数学中范畴论里的概念，指从任意范畴到集合范畴的一种特殊函子。这种函子将抽象的范畴表达成人们熟知的结构（即集合与函数），从而使得对集合范畴的了解可以尽可能应用到其它环境中。 从另外一个角度看，范畴的可表函子是随范畴而生的。因此，可表函子理论可以视作偏序集合理论中的上闭集合以及群论中的凱萊定理的极大的推广。 (zh) В теорії категорій, зображуваний функтор — функтор спеціального типу з довільної категорії в категорію множин. У певному сенсі, такі функтори задають опис категорії в термінах множин і функцій. (uk) |
| rdfs:label | Darstellbarkeit (Kategorientheorie) (de) Foncteur représentable (fr) 표현 가능 함자 (ko) Representable functor (en) Functor representável (pt) Представимый функтор (ru) Зображуваний функтор (uk) 可表函子 (zh) |
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