In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore, a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic. Note however that subobject classifiers are often much more complicated than the simple binary logic truth values {true, false}.
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| - Unterobjekt-Klassifizierer (de)
- Clasificador de subobjetos (es)
- 부분 대상 분류자 (ko)
- Subobject classifier (en)
- Классификатор подобъектов (ru)
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| rdfs:comment
| - En teoría de las categorías, un clasificador de subobjetos es un objeto especial Ω en una categoría; intuitivamente, los subobjetos de un objeto X corresponden a clases de equivalencia(por medio de iso) de los monomorfismos de X a Ω. (es)
- Unterobjekt-Klassifizierer werden im mathematischen Teilgebiet der Kategorientheorie untersucht. Es handelt sich um einen Monomorphismus, so dass jedes Unterobjekt auf diese Weise als Pullback dieses Monomorphismus längs eines eindeutig bestimmten Morphismus auftritt. Die Grundidee stammt aus der Kategorie der Mengen, in der eine Teilmenge mit der zugehörigen charakteristischen Funktion identifiziert werden kann. (de)
- In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore, a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic. Note however that subobject classifiers are often much more complicated than the simple binary logic truth values {true, false}. (en)
- 범주론에서 부분 대상 분류자(部分對象分類子, 영어: subobject classifier)는 주어진 대상의 각각의 부분 대상들을, 특정한 대상 로 가는 사상에 대응시킬 수 있도록 하는 구조이다. 집합론에서의 지시 함수의 개념을 일반화한 것으로, 부분 대상 분류자는 임의의 토포스에서 항상 존재한다. (ko)
- В теории категорий, классификатор подобъектов — специальный объект Ω категории; интуитивно, подобъекты X соответствуют морфизмам из X в Ω. Способ, которым он «классифицирует» объекты можно описать как присвоение некоторым элементам X значения «истина». (ru)
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| - En teoría de las categorías, un clasificador de subobjetos es un objeto especial Ω en una categoría; intuitivamente, los subobjetos de un objeto X corresponden a clases de equivalencia(por medio de iso) de los monomorfismos de X a Ω. (es)
- Unterobjekt-Klassifizierer werden im mathematischen Teilgebiet der Kategorientheorie untersucht. Es handelt sich um einen Monomorphismus, so dass jedes Unterobjekt auf diese Weise als Pullback dieses Monomorphismus längs eines eindeutig bestimmten Morphismus auftritt. Die Grundidee stammt aus der Kategorie der Mengen, in der eine Teilmenge mit der zugehörigen charakteristischen Funktion identifiziert werden kann. (de)
- In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore, a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic. Note however that subobject classifiers are often much more complicated than the simple binary logic truth values {true, false}. (en)
- 범주론에서 부분 대상 분류자(部分對象分類子, 영어: subobject classifier)는 주어진 대상의 각각의 부분 대상들을, 특정한 대상 로 가는 사상에 대응시킬 수 있도록 하는 구조이다. 집합론에서의 지시 함수의 개념을 일반화한 것으로, 부분 대상 분류자는 임의의 토포스에서 항상 존재한다. (ko)
- В теории категорий, классификатор подобъектов — специальный объект Ω категории; интуитивно, подобъекты X соответствуют морфизмам из X в Ω. Способ, которым он «классифицирует» объекты можно описать как присвоение некоторым элементам X значения «истина». (ru)
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