# Morphism

A Morphism is a structure-preserving mathematical mapping from one mathematical structure to another.

**Example(s):****See:**Set Theory, Function (Set Theory), Linear Algebra, Group Theory, Topology, Category Theory, Concrete Category.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/morphism Retrieved:2014-4-24.
- In many fields of mathematics,
**morphism**refers to a*structure-preserving mapping*from one mathematical structure to another. 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.

- In many fields of mathematics,