morphismn.

Brit.

/ˈmɔːfɪz(ə)m/, U.S.

/ˈmɔrˌfɪz(ə)m/

Origin: A borrowing from Greek, combined with an English element. Etymons: Greek μορϕή , -ism suffix.

Etymology: < ancient Greek μορϕή form (see -morph comb. form) + -ism suffix. Compare morph n.⁴, morphic adj. 2. In sense 2 probably after French morphisme (A. Grothendieck 1957, in Tôhoku Math. Jrnl. 9 122), ultimately after isomorphism n., homomorphism n., etc.

Biology.

1. The state or condition of being a morph (morph n.⁴); variance of form in an animal or plant species; polymorphism.

ΘΚΠ

the world > life > biology > biological processes > genetic activity > heredity or hereditary descent > [noun] > occurrence of variant forms

polymorphism1846

polymorphy1846

heteromorphism1874

polytypism1932

cline1938

topocline1939

polytypy1954

morphism1955

1955 J. S. Huxley in Heredity 9 2 I propose to introduce the term morphism and its derivatives, morphic and morph.

1960 C. T. Prime Lords & Ladies xii. 144 Mosaic spotting in several plants such as tomatoes and potatoes..is..a modification caused by the environment and not a true morphism.

1975 Jrnl. Zool. 177 336 From considerations of morphism, modality and sex-limitation, a descriptive classification of nine categories is advanced to encompass all situations involving pattern polymorphism and sexual dimorphism in butterflies.

1993 Oikos 67 433 The wing morphism of the overwintering (diapause) generation may differ from that of the summer (non-diapause) generation.

2. Mathematics. Any of a class of elements in a category (category n. Additions 3) which are associated with pairs of that category's objects, and which may be combined associatively under the operation of composition specified for that category. Frequently with distinguishing word denoting a particular type.The notion of a morphism represents an abstraction of that of a mapping between mathematical structures which preserves some aspect of their structure, as, say, homomorphisms do in the case of groups, rings, etc.

ΚΠ

1961 Ann. Math. 73 625 There is a morphism of functors λ returning us to the schema with which we started.

1986 Trans. Amer. Math. Soc. 297 564 If we do not specify otherwise, we will work with the category..whose objects are compactly generated spaces and whose morphisms are continuous maps.

1990 Amer. Math. Monthly 97 565 For each object X there is an identity morphism from it to itself.

2000 M. Scott Osborne Basic Homological Algebra vii. 173 The zero morphism is precisely the morphism which factors through ‘the’ zero object.

2014 D. I. Spivak Category Theory for Sci. v. 285 To describe a functor, we need to say what it does on objects..and what it does on morphisms.

This entry has been updated (OED Third Edition, December 2002; most recently modified version published online March 2022).

单词	morphism
释义	morphismn. Brit. /ˈmɔːfɪz(ə)m/, U.S. /ˈmɔrˌfɪz(ə)m/ Origin: A borrowing from Greek, combined with an English element. Etymons: Greek μορϕή , -ism suffix. Etymology: < ancient Greek μορϕή form (see -morph comb. form) + -ism suffix. Compare morph n.⁴, morphic adj. 2. In sense 2 probably after French morphisme (A. Grothendieck 1957, in Tôhoku Math. Jrnl. 9 122), ultimately after isomorphism n., homomorphism n., etc. Biology. 1. The state or condition of being a morph (morph n.⁴); variance of form in an animal or plant species; polymorphism. ΘΚΠ the world > life > biology > biological processes > genetic activity > heredity or hereditary descent > [noun] > occurrence of variant forms polymorphism1846 polymorphy1846 heteromorphism1874 polytypism1932 cline1938 topocline1939 polytypy1954 morphism1955 1955 J. S. Huxley in Heredity 9 2 I propose to introduce the term morphism and its derivatives, morphic and morph. 1960 C. T. Prime Lords & Ladies xii. 144 Mosaic spotting in several plants such as tomatoes and potatoes..is..a modification caused by the environment and not a true morphism. 1975 Jrnl. Zool. 177 336 From considerations of morphism, modality and sex-limitation, a descriptive classification of nine categories is advanced to encompass all situations involving pattern polymorphism and sexual dimorphism in butterflies. 1993 Oikos 67 433 The wing morphism of the overwintering (diapause) generation may differ from that of the summer (non-diapause) generation. 2. Mathematics. Any of a class of elements in a category (category n. Additions 3) which are associated with pairs of that category's objects, and which may be combined associatively under the operation of composition specified for that category. Frequently with distinguishing word denoting a particular type.The notion of a morphism represents an abstraction of that of a mapping between mathematical structures which preserves some aspect of their structure, as, say, homomorphisms do in the case of groups, rings, etc. ΚΠ 1961 Ann. Math. 73 625 There is a morphism of functors λ returning us to the schema with which we started. 1986 Trans. Amer. Math. Soc. 297 564 If we do not specify otherwise, we will work with the category..whose objects are compactly generated spaces and whose morphisms are continuous maps. 1990 Amer. Math. Monthly 97 565 For each object X there is an identity morphism from it to itself. 2000 M. Scott Osborne Basic Homological Algebra vii. 173 The zero morphism is precisely the morphism which factors through ‘the’ zero object. 2014 D. I. Spivak Category Theory for Sci. v. 285 To describe a functor, we need to say what it does on objects..and what it does on morphisms. This entry has been updated (OED Third Edition, December 2002; most recently modified version published online March 2022). > see also also refers to : -morphismcomb. form < n.1955 see also
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morphismn.

> see also