Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial or intuitive level, making the notion fairly powerful: it creates the opportunity to "translate" theorems between different kinds of mathematical structures, knowing that the essential meaning of those theorems is preserved under the translation.
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Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial or intuitive level, making the notion fairly powerful: it creates the opportunity to "translate" theorems between different kinds of mathematical structures, knowing that the essential meaning of those theorems is preserved under the translation.
has abstract
Die Äquivalenz von Kategorien ...... Äquivalenz zweier Kategorien.
@de
En mathématiques, plus précisé ...... de l'algèbre et de l'analyse.
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In category theory, an abstrac ...... than the equivalence concept.
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In de categorietheorie, een ab ...... deze vertaling bewaard blijft.
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Na teoria das categorias, equi ...... enos de isomorfismos naturais.
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Эквивале́нтность катего́рий в ...... мы с одних структур на другие.
@ru
在数学的一个抽象分支范畴论中,范畴的等价(equivalen ...... 概念,其中要求逆函子的严格性质,但这比“等价”概念用得要少。
@zh
数学、とりわけ圏論において、圏同値(けんどうち、英: equ ...... であることを要求するが、圏同値の概念に比べると実用性を欠く。
@ja
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Equivalence_of_categories
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equivalence+of+categories
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title
Equivalence of categories
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equivalence of categories
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wikiPageUsesTemplate
hypernym
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Die Äquivalenz von Kategorien ...... Äquivalenz zweier Kategorien.
@de
En mathématiques, plus précisé ...... lus pratique et plus courante.
@fr
In category theory, an abstrac ...... eserved under the translation.
@en
In de categorietheorie, een ab ...... deze vertaling bewaard blijft.
@nl
Na teoria das categorias, equi ...... enos de isomorfismos naturais.
@pt
Эквивале́нтность катего́рий в ...... мы с одних структур на другие.
@ru
在数学的一个抽象分支范畴论中,范畴的等价(equivalen ...... 概念,其中要求逆函子的严格性质,但这比“等价”概念用得要少。
@zh
数学、とりわけ圏論において、圏同値(けんどうち、英: equ ...... であることを要求するが、圏同値の概念に比べると実用性を欠く。
@ja
label
Equivalence of categories
@en
Equivalentie (categorietheorie)
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Equivalência de categorias
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Äquivalenz (Kategorientheorie)
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Équivalence de catégories
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Эквивалентность категорий
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圏同値
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范畴的等价
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범주의 동치
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