# Category Theory

# Description

From the Wikipedia:

"The study of categories is an attempt to capture what is commonly found in various classes of related mathematical structures.

**Instead of focusing merely on the individual objects (e.g. groups) possessing a given structure, category theory emphasizes the morphisms — the structure-preserving mappings — between these objects. It turns out that by studying these morphisms, we are able to learn more about the structure of the objects.** In the case of groups, the morphisms are the group homomorphisms. A group homomorphism between two groups "preserves the group structure" in a precise sense — it is a "process" taking one group to another, in a way that carries along information about the structure of the first group into the second group. The study of group homomorphisms then provides a tool for studying general properties of groups and consequences of the group axioms."
(http://en.wikipedia.org/wiki/Category_theory)