In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere (Lawvere, 1963 p. 36), although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories. Comma categories also guarantee the existence of some limits and colimits. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. The name persists even though standard notation has changed, since the use of a comma as an operator is potentially confusing, and e
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| - Comma category (en)
- Kommakategorie (de)
- Categoría coma (es)
- コンマ圏 (ja)
- 쉼표 범주 (ko)
- Категория запятой (ru)
- Categoria vírgula (pt)
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| - Eine Kommakategorie ist eine Konstruktion in der mathematischen Kategorientheorie, die 1963 von F. W. Lawvere eingeführt wurde. Der Name ergibt sich aus der ursprünglich von Lawvere verwendeten Notation. (de)
- En matemáticas, una categoría coma (siendo un caso especial una ) es una construcción en teoría de categorías. Facilita una forma distinta de estudiar morfismos: en lugar de simplemente relacionar los objetos de una categoría entre ellos, se estudian como objetos por sí mismos. Esta noción fue introducida en 1963 por F.W. Lawvere, aunque la técnica no fue generalmente conocida hasta muchos años después. El nombre original (comma category) proviene de la notación originalmente usada por Lawvere, que utilizaba el signo de puntuación coma. Aunque la notación original ha cambiado con el tiempo, el nombre persiste. (es)
- 범주론에서 쉼표 범주(-標範疇, 영어: comma category)는 같은 공역을 갖는 두 함자로부터 정의되고, 함자들의 공역의 사상들을 대상으로 하는 범주이다. (ko)
- 圏論においてコンマ圏（こんまけん、英: comma category）とは、圏の構成法の一つを言う。特定の構成はスライス圏（slice category）とも呼ばれる。コンマ圏という名称は1963年にウィリアム・ローヴェアが句読点コンマにちなんで使用した表記に由来する。 普遍性、極限、余極限を含む幾つかの概念は、コンマ圏として扱うことができる。 (ja)
- Na teoria das categorias, uma categoria vírgula (em inglês, comma category) é uma categoria cujos objetos correspondem a certos morfismos de outra categoria. Sua definição foi introduzida por William Lawvere, em 1963; o nome provém de uma de suas notações, que usa o sinal de pontuação vírgula. (pt)
- В теории категорий, категория запятой — специальная конструкция, предоставляющая способ изучения морфизмов не как соотнесений объектов категории друг с другом, а как самостоятельных объектов. Название «категория запятой» появилось из-за первоначального (придуманного Ловером) обозначения, которое включало в себя знак запятой. Впоследствии стандартное обозначение изменилось из соображений удобства. (ru)
- In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere (Lawvere, 1963 p. 36), although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories. Comma categories also guarantee the existence of some limits and colimits. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. The name persists even though standard notation has changed, since the use of a comma as an operator is potentially confusing, and e (en)
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| - Eine Kommakategorie ist eine Konstruktion in der mathematischen Kategorientheorie, die 1963 von F. W. Lawvere eingeführt wurde. Der Name ergibt sich aus der ursprünglich von Lawvere verwendeten Notation. (de)
- In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere (Lawvere, 1963 p. 36), although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories. Comma categories also guarantee the existence of some limits and colimits. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. The name persists even though standard notation has changed, since the use of a comma as an operator is potentially confusing, and even Lawvere dislikes the uninformative term "comma category" (Lawvere, 1963 p. 13). (en)
- En matemáticas, una categoría coma (siendo un caso especial una ) es una construcción en teoría de categorías. Facilita una forma distinta de estudiar morfismos: en lugar de simplemente relacionar los objetos de una categoría entre ellos, se estudian como objetos por sí mismos. Esta noción fue introducida en 1963 por F.W. Lawvere, aunque la técnica no fue generalmente conocida hasta muchos años después. El nombre original (comma category) proviene de la notación originalmente usada por Lawvere, que utilizaba el signo de puntuación coma. Aunque la notación original ha cambiado con el tiempo, el nombre persiste. (es)
- 범주론에서 쉼표 범주(-標範疇, 영어: comma category)는 같은 공역을 갖는 두 함자로부터 정의되고, 함자들의 공역의 사상들을 대상으로 하는 범주이다. (ko)
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