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In der Mathematik ist eine symmetrische monoidale Kategorie eine monoidale Kategorie (d. h. eine Kategorie, in der ein "Tensorprodukt" definiert ist), deren Tensorprodukt symmetrisch ist (d. h. man hat einen natürlichen Isomorphismus zwischen und für alle Objekte und ). Ein typisches Beispiele ist die Kategorie der Vektorräume über einem gegebenen Körper. (de) In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" is defined) such that the tensor product is symmetric (i.e. is, in a certain strict sense, naturally isomorphic to for all objects and of the category). One of the prototypical examples of a symmetric monoidal category is the category of vector spaces over some fixed field k, using the ordinary tensor product of vector spaces. (en) 범주론에서 대칭 모노이드 범주(對稱monoid範疇, 영어: symmetric monoidal category)는 동형 사상 아래 결합 법칙과 교환 법칙이 성립하고, 동형 사상 아래 항등원이 존재하는 이항 연산을 갖는 범주이다. (교환 법칙이 성립하지 못할 수 있는) 모노이드 범주의 개념의 특수한 경우이다. (ko) В теории категорий симметричная моноидальная категория — это моноидальная категория, в которой операция тензорного произведения «настолько коммутативна, насколько это возможно». В симметричной моноидальной категории для любых объектов выбран изоморфизм , причём все эти изоморфизмы вместе образуют естественное семейство. (ru) |
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Symmetric monoidal category (en) |
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In der Mathematik ist eine symmetrische monoidale Kategorie eine monoidale Kategorie (d. h. eine Kategorie, in der ein "Tensorprodukt" definiert ist), deren Tensorprodukt symmetrisch ist (d. h. man hat einen natürlichen Isomorphismus zwischen und für alle Objekte und ). Ein typisches Beispiele ist die Kategorie der Vektorräume über einem gegebenen Körper. (de) In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" is defined) such that the tensor product is symmetric (i.e. is, in a certain strict sense, naturally isomorphic to for all objects and of the category). One of the prototypical examples of a symmetric monoidal category is the category of vector spaces over some fixed field k, using the ordinary tensor product of vector spaces. (en) 범주론에서 대칭 모노이드 범주(對稱monoid範疇, 영어: symmetric monoidal category)는 동형 사상 아래 결합 법칙과 교환 법칙이 성립하고, 동형 사상 아래 항등원이 존재하는 이항 연산을 갖는 범주이다. (교환 법칙이 성립하지 못할 수 있는) 모노이드 범주의 개념의 특수한 경우이다. (ko) В теории категорий симметричная моноидальная категория — это моноидальная категория, в которой операция тензорного произведения «настолько коммутативна, насколько это возможно». В симметричной моноидальной категории для любых объектов выбран изоморфизм , причём все эти изоморфизмы вместе образуют естественное семейство. (ru) |
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Symmetrische monoidale Kategorie (de) 대칭 모노이드 범주 (ko) Symmetric monoidal category (en) Симметричная моноидальная категория (ru) |
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