About: Internal category

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In mathematics, more specifically in category theory, internal categories are a generalisation of the notion of small category, and are defined with respect to a fixed . If the ambient category is taken to be the category of sets then one recovers the theory of small categories. In general, internal categories consist of a pair of objects in the ambient category—thought of as the 'object of objects' and 'object of morphisms'—together with a collection of morphisms in the ambient category satisfying certain identities. Group objects, are common examples of internal categories.

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  • In mathematics, more specifically in category theory, internal categories are a generalisation of the notion of small category, and are defined with respect to a fixed . If the ambient category is taken to be the category of sets then one recovers the theory of small categories. In general, internal categories consist of a pair of objects in the ambient category—thought of as the 'object of objects' and 'object of morphisms'—together with a collection of morphisms in the ambient category satisfying certain identities. Group objects, are common examples of internal categories. There are notions of internal functors and natural transformations that make the collection of internal categories in a fixed category into a 2-category. (en)
  • 범주론에서 내적 범주(內的範疇, 영어: internal category)는 작은 범주의 정의에서 사용되는 집합의 범주를 대체하여, 임의의 범주 속에서 범주처럼 작동하는 구조이다. 작은 범주의 개념의 일반화이다. (ko)
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  • internal+category (en)
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  • Internal category (en)
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  • 범주론에서 내적 범주(內的範疇, 영어: internal category)는 작은 범주의 정의에서 사용되는 집합의 범주를 대체하여, 임의의 범주 속에서 범주처럼 작동하는 구조이다. 작은 범주의 개념의 일반화이다. (ko)
  • In mathematics, more specifically in category theory, internal categories are a generalisation of the notion of small category, and are defined with respect to a fixed . If the ambient category is taken to be the category of sets then one recovers the theory of small categories. In general, internal categories consist of a pair of objects in the ambient category—thought of as the 'object of objects' and 'object of morphisms'—together with a collection of morphisms in the ambient category satisfying certain identities. Group objects, are common examples of internal categories. (en)
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  • Internal category (en)
  • 내적 범주 (ko)
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