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In mathematics, specifically category theory, a family of generators (or family of separators) of a category is a collection of objects in , such that for any two distinct morphisms in , that is with , there is some in and some morphism such that If the collection consists of a single object , we say it is a generator (or separator). Generators are central to the definition of Grothendieck categories. The dual concept is called a cogenerator or coseparator.

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  • Generator und Kogenerator sind Begriffe aus dem mathematischen Teilgebiet der Kategorientheorie. Es handelt sich um Objekte einer Kategorie, die zu beliebigen Objekten der Kategorie in einer bestimmten Beziehung stehen. Statt Generator und Kogenerator findet man auch die Bezeichnungen Separator und Koseparator. (de)
  • In mathematics, specifically category theory, a family of generators (or family of separators) of a category is a collection of objects in , such that for any two distinct morphisms in , that is with , there is some in and some morphism such that If the collection consists of a single object , we say it is a generator (or separator). Generators are central to the definition of Grothendieck categories. The dual concept is called a cogenerator or coseparator. (en)
  • Na teoria das categorias, um separador, família separadora, gerador ou família geradora para uma categoria C é uma família S de objetos de C, tal que, para quaisquer morfismos paralelos f, g : c → d em C que sejam "indistinguíveis por morfismos a partir de S", isto é, para quaisquer s ∈ S e h : s → c, f ∘ h = g ∘ h, então f = g. Dualmente, T é cosseparador ou cogerador para C quando para quaisquer t ∈ T e h : d → t, h ∘ f = h ∘ g, implica f = g. (pt)
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  • Generator und Kogenerator sind Begriffe aus dem mathematischen Teilgebiet der Kategorientheorie. Es handelt sich um Objekte einer Kategorie, die zu beliebigen Objekten der Kategorie in einer bestimmten Beziehung stehen. Statt Generator und Kogenerator findet man auch die Bezeichnungen Separator und Koseparator. (de)
  • In mathematics, specifically category theory, a family of generators (or family of separators) of a category is a collection of objects in , such that for any two distinct morphisms in , that is with , there is some in and some morphism such that If the collection consists of a single object , we say it is a generator (or separator). Generators are central to the definition of Grothendieck categories. The dual concept is called a cogenerator or coseparator. (en)
  • Na teoria das categorias, um separador, família separadora, gerador ou família geradora para uma categoria C é uma família S de objetos de C, tal que, para quaisquer morfismos paralelos f, g : c → d em C que sejam "indistinguíveis por morfismos a partir de S", isto é, para quaisquer s ∈ S e h : s → c, f ∘ h = g ∘ h, então f = g. Dualmente, T é cosseparador ou cogerador para C quando para quaisquer t ∈ T e h : d → t, h ∘ f = h ∘ g, implica f = g. (pt)
rdfs:label
  • Generator und Kogenerator (de)
  • Generator (category theory) (en)
  • Separador (teoria das categorias) (pt)
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