# morphism

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*See also:*

**-morphism**

## Contents

## English[edit]

### Etymology[edit]

Generalised from *isomorphism*, etc.

### Noun[edit]

**morphism** (*plural* **morphisms**)

- (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. 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.

- 1°
**1992**, Terrance Brown (translator), Gil Henriques,*Chapter 13:*, Terrance Brown (translator), Jean Piaget, Gil Henriques, Edgar Ascher (editors),**Morphisms**and Transformations in the Construction of Invariants, page 198,**Morphisms**and Categories: Comparing and Transforming- 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.

- In certain extreme cases in mathematics, the synthesis of
**2007**November, Steven Dale Cutkosky,*Toroidalization of Dominant*, Memoirs of the American Mathematical Society, Volume 190, Number 890, page 3,**Morphisms**of 3-Folds- 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**].

- The proof of toroidalization of

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