Category theory

Category theory is a big, complicated, confusing area of mathematics concerned with "Categories".

Introduction
A category can be thought of as- but is not equivalent to- a labeled digraph: a set of nodes containing values with directed edges mapping nodes to other nodes. In the more general way of thought, a category is a set of "objects"- which can be any type of arbitrary thing- with "arrows" (also called "morphisms") between them mapping one to another. An arrow represents some sort of transformation between a "domain"- the object from which the arrow originates- and the "codomain"- the destination object.

Categories also have some sort of operation for composing arrows, written. This leads to the property that, if there is are two arrows  and , then there is another arrow. This should be reminiscent of function composition in other areas of mathematics, but represents a more general concept. Note that it is required that  is associative- that is,.

The final requirement for a category is that every object has a left and a right "identity object". For some morphism, The right identity object has the property that  , and the left identity has the property