Fundamental concepts

The 3 fundamental concepts at the heart of category theory:

• Category

• Functor

• Natural Transformation

A category is the main object of concern, it consists of a network of arrow-connected objects.

A functor is a mapping between categories that preserves strutcure. A functor maps both objects and arrows in a category; it maps objects to objects, and arrows to arrows.

A natural transformation is a another mapping, this time between functors.

Acquired terminology:

• category theory

• category

• object

• arrow, morphism

• composition of arrows

• associativity of arrow composition

• identity arrow, identity wrt arrow composition

• functor

• natural transformation