different between morphism vs polymorphism

English

Etymology

Generalised from isomorphism, etc.

Noun

morphism (plural morphisms)

1. (mathematics, category theory) (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.
   • 1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. ?encov, 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.

   • 2007 November, Steven Dale Cutkosky, Toroidalization of Dominant Morphisms of 3-Folds, Memoirs of the American Mathematical Society, Volume 190, Number 890, page 3,

     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].

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

Synonyms

• (category theory): arrow, map

Derived terms

• bimorphism
• epimorphism
• monomorphism

Related terms

• automorphism
• diffeomorphism
• homeomorphism
• homomorphism
• isomorphism

Translations

See also

• bijection
• function
• functor
• isometry
• measurable function

English

Etymology

From poly- +? -morphism.

Pronunciation

• (UK) IPA^(key): /p?l??m??f?z(?)m/
• (US) enPR: päl-?-môr?f?z-?m, IPA^(key): /p?li?m??f?z(?)m/

Noun

polymorphism (countable and uncountable, plural polymorphisms)

1. The ability to assume different forms or shapes.
2. (biology) The coexistence, in the same locality, of two or more distinct forms independent of sex, not connected by intermediate gradations, but produced from common parents.
3. (object-oriented programming) The feature pertaining to the dynamic treatment of data elements based on their type, allowing for an instance of a method to have several definitions.
4. (mathematics, type theory) The property of certain typed formal systems of allowing for the use of type variables and binders/quantifiers over those type variables; likewise, the property of certain expressions (within such typed formal systems) of making use of at least one such typed variable.
5. (crystallography) The ability of a solid material to exist in more than one form or crystal structure; pleomorphism.
6. (genetics) The regular existence of two or more different genotypes within a given species or population; also, variability of amino acid sequences within a gene's protein.
   • 1999, Matt Ridley, Genome, Harper Perennial 2004, p. 137:

     Since 1990 they have found an entirely new role: they promise understanding of how and why our genes are all so different. They hold the key to human polymorphism.

   • 2004, Richard Dawkins, The Ancestor's Tale, Phoenix 2005, p. 63:

     Some polymorphisms can be quite stable – so stable that they span the change from an ancestral to a descendant species.

Hyponyms

Related terms

Translations

See also

• RFLP
• riflip

References

• polymorphism on Wikipedia.Wikipedia