> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/450-category-theory/01-fundamentals/03-fundamentals.md).

# 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