morphism

Noun

morphism (plural morphisms)

1. (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.
   • 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.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...
   • 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.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...
2. Being or having distinct variants of a plant or animal species in the same locale; polymorphism.
   • 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.2010, T.J. Pandian, Sexuality in Fishes, page 51