morphism
Language: English
Part of speech: noun
Pronunciation: ipa: /ˈmɔːfɪzəm/
ipa: /ˈmɔɹfɪzəm/
rhymes: -ɔː(ɹ)fɪzəm
Forms: form: morphisms
Etymology: Generalised from isomorphism, etc.
Senses: examples: text: 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.
text: 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.
text: 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].
ref: 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:
topics: category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: (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.
examples: text: 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.
ref: 2010, T.J. Pandian, Sexuality in Fishes, page 51:
topics: biology
natural-sciences
glosses: Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
Synonyms: topics: category-theory
mathematics
computing
engineering
sciences
physical-sciences
natural-sciences
word: arrow
topics: category-theory
mathematics
computing
engineering
sciences
physical-sciences
natural-sciences
word: map
Derived terms: allelomorphism
anamorphism
antimorphism
apomorphism
automorphism
bimorphism
catamorphism
classifying morphism
coconstant morphism
comorphism
constant morphism
contactomorphism
diagonal morphism
diffeomorphism
epimorphism
homeomorphism
homomorphism
hylomorphism
identity morphism
isomorphism
monomorphism
morphism set
multimorphism
orthomorphism
transmorphism
twist morphism
universal morphism
zero morphism
Related terms: -morphism
bijection
function
functor
isometry
measurable function