#readwise # Category Theory - Wikipedia  ## Metadata - Author: [[en.wikipedia.org]] - Full Title: Category Theory - Wikipedia - URL: https://en.wikipedia.org/wiki/Category_theory ## Highlights Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of 20th century in their foundational work on algebraic topology. --- **A category is formed by two sorts of objects, the objects of the category, and the morphisms, which relate two objects called the source and the target of the morphism. One often says that a morphism is an arrow that maps its source to its target.** Morphisms can be composed if the target of the first morphism equals the source of the second one, and morphism composition has similar properties as function composition (associativity and existence of identity morphisms). **Morphisms are often some sort of function, but this is not always the case.** For example, a monoid may be viewed as a category with a single object, whose morphisms are the elements of the monoid. ^qp7cz1 ---