In category theory, a regular category is a category with finite limits and coequalizers of a pair of morphisms called kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence of images, without requiring additivity. At the same time, regular categories provide a foundation for the study of a fragment of first-order logic, known as regular logic.
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| - 정칙 범주 (ko)
- Regelmatige categorie (nl)
- Regular category (en)
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| - In category theory, a regular category is a category with finite limits and coequalizers of a pair of morphisms called kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence of images, without requiring additivity. At the same time, regular categories provide a foundation for the study of a fragment of first-order logic, known as regular logic. (en)
- 범주론에서 정칙 범주(正則範疇, 영어: regular category)는 모든 유한 극한을 갖고, 모든 사상을 그 치역으로의 전사 사상과 치역에서 공역으로 가는 단사 사상으로 유일하게 분해할 수 있는 범주이다. (ko)
- In de categorietheorie, een abstract deelgebied van de wiskunde, is een regelmatige categorie een categorie met eindige limieten en van kernparen, die voldoen aan zekere exactheids-voorwaarden. Op die manier vangt men in regelmatige vele eigenschappen van abelse categorieën, zoals het bestaan van beelden, zonder dat er additiviteit vereist is. Tegelijkertijd leggen regelmatige categorieën een fundament voor de studie van een deel van de eerste-orde logica, dat bekendstaat als regelmatige logica. (nl)
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| - In category theory, a regular category is a category with finite limits and coequalizers of a pair of morphisms called kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence of images, without requiring additivity. At the same time, regular categories provide a foundation for the study of a fragment of first-order logic, known as regular logic. (en)
- 범주론에서 정칙 범주(正則範疇, 영어: regular category)는 모든 유한 극한을 갖고, 모든 사상을 그 치역으로의 전사 사상과 치역에서 공역으로 가는 단사 사상으로 유일하게 분해할 수 있는 범주이다. (ko)
- In de categorietheorie, een abstract deelgebied van de wiskunde, is een regelmatige categorie een categorie met eindige limieten en van kernparen, die voldoen aan zekere exactheids-voorwaarden. Op die manier vangt men in regelmatige vele eigenschappen van abelse categorieën, zoals het bestaan van beelden, zonder dat er additiviteit vereist is. Tegelijkertijd leggen regelmatige categorieën een fundament voor de studie van een deel van de eerste-orde logica, dat bekendstaat als regelmatige logica. (nl)
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