Category Theory

Category theory is abstract, about as abstract as mathematics gets.

It is the study of systems of related objects. The relations between the objects under study are called maps (also arrows or morphisms)

Maps bind Objects together in a relationship.

Often Objects are Represented by Letters and Maps by Arrow, such as:

       f       g
   A  ---> B  -->  C



where we have objects A, B and C, and arrows f & g.

A and B are related through f & B and C are related through g.

Category theory born out of the studies in

Algebraic Topology was formulated precisely in the 1940's by Samuel Eilenberg & Saunders Mac Lane.

Categories are themselves Objects.

Functors are maps between Categories.

Natural Transformations are maps between Functors.

Often the term Homomorphism is used, I like to think of it as nothing more than meaning a general morphism.

Categories

http:///wiki/?categorytheory

08dec16   admin