意味 | 共起表現 |
morphismとは 意味・読み方・使い方
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意味・対訳 数学の多くの分野において、型射あるいは射(しゃ、英: morphism; モルフィズム)は、ある数学的構造を持つ数学的対象から別の数学的対象への「構造を保つ」写像の意味で用いられる(準同型)。
Wiktionary英語版での「morphism」の意味 |
morphism
語源
Generalised from isomorphism, etc.
名詞
morphism (複数形 morphisms)
- (mathematics, category theory) (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.
- 1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50,
- 1° The composition of two morphisms is defined if and only if the final object of the first morphism is the initial object of the second. This composition is also a morphism, whose initial object is the initial object of the first morphism and whose final object is the final object of the second.
- 1992, Terrance Brown (translator), Gil Henriques, Chapter 13: Morphisms and Transformations in the Construction of Invariants, Terrance Brown (translator), Jean Piaget, Gil Henriques, Edgar Ascher (editors), Morphisms and Categories: Comparing and Transforming, page 198,
- In certain extreme cases in mathematics, the synthesis of morphisms and of transformations is so intimate that one can speak of a veritable fusion. […] Essentially, categories are sets of morphisms organized into operatory systems.
- 2007 November, Steven Dale Cutkosky, Toroidalization of Dominant Morphisms of 3-Folds, Memoirs of the American Mathematical Society, Volume 190, Number 890, page 3,
- 1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50,
- (biology) Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
同意語
- (category theory): arrow, map
派生語
- bimorphism
- epimorphism
- monomorphism
-morphism
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