Difference between revisions of "Morphism"
Karl Jones (Talk | contribs) (Created page with "In many fields of mathematics, '''morphism''' refers to a structure-preserving map from one mathematical structure to another. == Description ==...") |
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* [[Category theory]] | * [[Category theory]] | ||
* [[Isomorphism]] | * [[Isomorphism]] | ||
| + | * [[Linear map]] | ||
* [[Map (mathematics)]] | * [[Map (mathematics)]] | ||
| + | * [[Mathematical object]] | ||
* [[Mathematical structure]] | * [[Mathematical structure]] | ||
* [[Normal morphism]] | * [[Normal morphism]] | ||
Latest revision as of 06:13, 16 September 2016
In many fields of mathematics, morphism refers to a structure-preserving map from one mathematical structure to another.
Description
The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in topology, continuous functions, and so on.
In category theory, morphism is a broadly similar idea, but somewhat more abstract: the mathematical objects involved need not be sets, and the relationship between them may be something more general than a map.
The study of morphisms and of the structures (called "objects") over which they are defined is central to category theory. Much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure-preserving functions. In category theory, morphisms are sometimes also called arrows.
See also
- Automorphism
- Category (mathematics)
- Category theory
- Isomorphism
- Linear map
- Map (mathematics)
- Mathematical object
- Mathematical structure
- Normal morphism
- Zero morphism
External links
- Morphism @ Wikipedia.org
