# 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
