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In category theory, an end of a functor is a universal extranatural transformation from an object e of X to S. More explicitly, this is a pair , where e is an object of X and is an extranatural transformation such that for every extranatural transformation there exists a unique morphism of X with for every object a of C. By abuse of language the object e is often called the end of the functor S (forgetting ) and is written Characterization as limit: If X is complete and C is small, the end can be described as the equalizer in the diagram

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  • Ende (Kategorientheorie) (de)
  • Fin (théorie des catégories) (fr)
  • End (category theory) (en)
  • 끝 (범주론) (ko)
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  • Im mathematischen Teilgebiet der Kategorientheorie ist ein Ende ein spezieller Limes. (de)
  • En mathématiques, une fin d'un foncteur est une généralisation du concept de limite. Les fins et leurs duales, les cofins, sont généralement notées avec le s long de l'intégrale. La notion de fin apparaît naturellement dans les extensions de Kan en théorie des catégories enrichies, et dans l'étude des . En particulier, la fin d'un foncteur, vu comme distributeur, correspond au (en) sur lequel l'action à droite et l'action à gauche coïncident. (fr)
  • ( 다른 뜻에 대해서는 끝 대상 문서를 참고하십시오.) 범주론에서 끝(영어: end 엔드[*])과 쌍대끝(雙對-, 영어: coend 코엔드[*])은 어떤 데이터들을 범주론적으로 “이어붙이는” 연산이다. (ko)
  • In category theory, an end of a functor is a universal extranatural transformation from an object e of X to S. More explicitly, this is a pair , where e is an object of X and is an extranatural transformation such that for every extranatural transformation there exists a unique morphism of X with for every object a of C. By abuse of language the object e is often called the end of the functor S (forgetting ) and is written Characterization as limit: If X is complete and C is small, the end can be described as the equalizer in the diagram (en)
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  • Im mathematischen Teilgebiet der Kategorientheorie ist ein Ende ein spezieller Limes. (de)
  • In category theory, an end of a functor is a universal extranatural transformation from an object e of X to S. More explicitly, this is a pair , where e is an object of X and is an extranatural transformation such that for every extranatural transformation there exists a unique morphism of X with for every object a of C. By abuse of language the object e is often called the end of the functor S (forgetting ) and is written Characterization as limit: If X is complete and C is small, the end can be described as the equalizer in the diagram where the first morphism being equalized is induced by and the second is induced by . (en)
  • En mathématiques, une fin d'un foncteur est une généralisation du concept de limite. Les fins et leurs duales, les cofins, sont généralement notées avec le s long de l'intégrale. La notion de fin apparaît naturellement dans les extensions de Kan en théorie des catégories enrichies, et dans l'étude des . En particulier, la fin d'un foncteur, vu comme distributeur, correspond au (en) sur lequel l'action à droite et l'action à gauche coïncident. (fr)
  • ( 다른 뜻에 대해서는 끝 대상 문서를 참고하십시오.) 범주론에서 끝(영어: end 엔드[*])과 쌍대끝(雙對-, 영어: coend 코엔드[*])은 어떤 데이터들을 범주론적으로 “이어붙이는” 연산이다. (ko)
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