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In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology.

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  • Triangulierte Kategorie (de)
  • Catégorie triangulée (fr)
  • 삼각 분할 범주 (ko)
  • Triangulated category (en)
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  • Triangulierte Kategorie ist ein Begriff aus der homologischen Algebra. Triangulierte Kategorien bieten einen gemeinsamen Rahmen für derivierte Kategorien und für die stabilen Modulkategorien der Darstellungstheorie. Ursprünglich wurden sie durch Verdier eingeführt, um derivierte Funktoren der algebraischen Geometrie zu studieren. (de)
  • En mathématiques, une catégorie triangulée est une catégorie dotée d'une structure supplémentaire. De telles catégories ont été suggérées par Alexander Grothendieck et développées par Jean-Louis Verdier dans sa thèse de 1963 pour traiter les catégories dérivées. La notion de t-structure, qui y est directement liée, permet de reconstruire (en un sens partiel) une catégorie à partir d'une catégorie dérivée. (fr)
  • 호몰로지 대수학에서 삼각 분할 범주(三角分割範疇, 영어: triangulated category)는 유도 범주 및 안정 호모토피 범주와 유사한 성질을 가지는 범주이다. 이 위에 일반적인 코호몰로지 함자의 개념을 정의할 수 있다. (ko)
  • In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. (en)
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