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- In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these categories was further developed in Pierre Gabriel's seminal thesis in 1962. To every algebraic variety one can associate a Grothendieck category , consisting of the quasi-coherent sheaves on . This category encodes all the relevant geometric information about , and can be recovered from (the Gabriel–Rosenberg reconstruction theorem). This example gives rise to one approach to noncommutative algebraic geometry: the study of "non-commutative varieties" is then nothing but the study of (certain) Grothendieck categories. (en)
- 호몰로지 대수학에서 그로텐디크 아벨 범주(Grothendieck Abel範疇, 영어: Grothendieck Abelian category)는 특별히 좋은 성질을 가져, 호몰로지 대수학을 전개하기 간편한 아벨 범주이다. (ko)
- In de homologische algebra en de categorietheorie, deelgebieden van de wiskunde, is een Grothendieck-categorie een bepaalde vorm van een abelse categorie, die in 1957 door Alexander Grothendieck werd geïntroduceerd om op een uniforme manier de machinerie van de homologische algebra voor modulen en voor schoven te ontwikkelen. (nl)
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- Grothendieck_category (en)
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- Grothendieck category (en)
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- 호몰로지 대수학에서 그로텐디크 아벨 범주(Grothendieck Abel範疇, 영어: Grothendieck Abelian category)는 특별히 좋은 성질을 가져, 호몰로지 대수학을 전개하기 간편한 아벨 범주이다. (ko)
- In de homologische algebra en de categorietheorie, deelgebieden van de wiskunde, is een Grothendieck-categorie een bepaalde vorm van een abelse categorie, die in 1957 door Alexander Grothendieck werd geïntroduceerd om op een uniforme manier de machinerie van de homologische algebra voor modulen en voor schoven te ontwikkelen. (nl)
- In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these categories was further developed in Pierre Gabriel's seminal thesis in 1962. (en)
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- Grothendieck category (en)
- 그로텐디크 아벨 범주 (ko)
- Grothendieck-categorie (nl)
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