morphismとは 意味・読み方・使い方

語源

Generalised from isomorphism, etc.

発音

• (Received Pronunciation) IPA: /ˈmɔːfɪzəm/
• (General American) IPA: /ˈmɔɹfɪzəm/
• 韻: -ɔː(ɹ)fɪzəm

名詞

morphism (plural morphisms)

1. (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”, in Memoirs of the, volume 190, number 890, American Mathematical Society, page 3:

     The proof of toroidalization of morphisms of 3-folds to surfaces in [C3] breaks up into two parts: a reduction to prepared morphisms and then a proof of toroidalization of prepared morphisms from n-folds to [surfaces] in [CK].

2. (biology) Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
   • 2010, T.J. Pandian, Sexuality in Fishes, page 51:

     Briefly, the yellow morphic males can change their status from paired to satellite and from satellite to the paired one. However, they cannot cross into the status of the red morph. […] The colour morphism of males is proved to be irreversible after its expression at an early stage of ontogeny.

同意語

• (category theory): arrow, map

使用する際の注意点

In mathematics, this word is largely interchangeable with homomorphism. However, one uses morphism almost exclusively in the context of category theory, while homomorphism is more common in algebra.

派生語

関連する語

参考

• bijection
• function
• functor
• isometry
• measurable function

発音

接尾辞

-morphism

1. The state of having a specified shape or form.

派生語

関連する語