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F-algebra je v teorii kategorií dvojice , kde je nosný objekt a morfismus . F-algebry jsou zobecněním abstraktních algebraických struktur. Homomorfismus mezi dvěma F-algebrami a je morfismus takový, že . F-algebry spolu s homomorfismy tvoří kategorii. Má-li tato kategorie počáteční objekt, unikátní morfismy z toho objektu se nazývají . Katamorfismy jsou zobecněním operace ve funkcionálním programování. Příklad: signatura grup je dána funktorem . (cs) Eine F-Algebra ist eine Struktur, welche allein auf Funktoreigenschaften beruht. Dual zum Begriff der F-Algebra ist der der (de) In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature. F-algebras can also be used to represent data structures used in programming, such as lists and trees. The main related concepts are initial F-algebras which may serve to encapsulate the induction principle, and the dual construction F-coalgebras. (en) 数学の特に圏論におけるF-代数（エフだいすう、英: F-algebra）は、（自己）関手 F に従って定義される構造の一つで、リストや木構造のようなプログラミングで使われるデータ構造を表現するのに利用できる。 F-始代数は、数学的帰納法の原理を捉えたものと考えることができる。文脈上紛れの虞が無い場合は、函手 F を明示するための接頭辞 F- を省略して単に代数ということがある。 F-代数は F-余代数の双対である。 (ja) В теории категорий -алгебра — это алгебраическая структура, связанная с функтором . -алгебры можно использовать в программировании для представления структур данных, таких как списки и деревья. (ru) У математиці, і особливо у теорії категорій, -алгебра — це алгебраїчна структура, пов'язана з функтором . (uk) |
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http://tunes.org/wiki/algebra_20and_20coalgebra.html https://kodu.ut.ee/~varmo/papers/thesis.pdf http://homepages.inf.ed.ac.uk/wadler/papers/free-rectypes/free-rectypes.txt https://www.cs.ru.nl/~bart/PAPERS/JR.pdf https://www.schoolofhaskell.com/user/bartosz/understanding-algebras https://web.archive.org/web/20190427054226/http:/tunes.org/wiki/algebra_20and_20coalgebra.html https://web.archive.org/web/20200804134826/https:/www.schoolofhaskell.com/user/bartosz/understanding-algebras https://web.archive.org/web/20201130055213/http:/homepages.inf.ed.ac.uk/wadler/papers/free-rectypes/free-rectypes.txt https://web.archive.org/web/20201130102325/https:/kodu.ut.ee/~varmo/papers/thesis.pdf https://web.archive.org/web/20210212014629/http:/www.cs.ru.nl/~bart/PAPERS/JR.pdf |
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F-algebra je v teorii kategorií dvojice , kde je nosný objekt a morfismus . F-algebry jsou zobecněním abstraktních algebraických struktur. Homomorfismus mezi dvěma F-algebrami a je morfismus takový, že . F-algebry spolu s homomorfismy tvoří kategorii. Má-li tato kategorie počáteční objekt, unikátní morfismy z toho objektu se nazývají . Katamorfismy jsou zobecněním operace ve funkcionálním programování. Příklad: signatura grup je dána funktorem . (cs) Eine F-Algebra ist eine Struktur, welche allein auf Funktoreigenschaften beruht. Dual zum Begriff der F-Algebra ist der der (de) In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature. F-algebras can also be used to represent data structures used in programming, such as lists and trees. The main related concepts are initial F-algebras which may serve to encapsulate the induction principle, and the dual construction F-coalgebras. (en) 数学の特に圏論におけるF-代数（エフだいすう、英: F-algebra）は、（自己）関手 F に従って定義される構造の一つで、リストや木構造のようなプログラミングで使われるデータ構造を表現するのに利用できる。 F-始代数は、数学的帰納法の原理を捉えたものと考えることができる。文脈上紛れの虞が無い場合は、函手 F を明示するための接頭辞 F- を省略して単に代数ということがある。 F-代数は F-余代数の双対である。 (ja) В теории категорий -алгебра — это алгебраическая структура, связанная с функтором . -алгебры можно использовать в программировании для представления структур данных, таких как списки и деревья. (ru) У математиці, і особливо у теорії категорій, -алгебра — це алгебраїчна структура, пов'язана з функтором . (uk) |
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