Meaning of morphism | Babel Free

Definitions

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.
2. Being or having distinct variants of a plant or animal species in the same locale; polymorphism.

Equivalents

Examples

“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.”

“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].”

“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.”

CEFR level