(mathematics,category theory) (formally) Anarrow in acategory; (less formally) an abstraction that generalises amap 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 twomorphisms is defined if and only if the final object of the firstmorphism is the initial object of the second. This composition is also amorphism, whose initial object is the initial object of the firstmorphism 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 ofmorphisms and of transformations is so intimate that one can speak of a veritable fusion.[…]Essentially, categories are sets ofmorphisms organized into operatory systems.
2007 November, Steven Dale Cutkosky, “Toroidalization of DominantMorphisms of 3-Folds”, inMemoirs of the, volume190, number890,American Mathematical Society,page 3:
The proof of toroidalization ofmorphisms of 3-folds to surfaces in [C3] breaks up into two parts: a reduction to preparedmorphisms and then a proof of toroidalization of preparedmorphisms fromn-folds to [surfaces] in [CK].
(biology) Being or having distinct variants of a plant or animalspecies in the same locale;polymorphism.
2010, T.J. Pandian,Sexuality in Fishes, page51:
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 colourmorphism of males is proved to be irreversible after its expression at an early stage of ontogeny.
