Category theory is the algebra of functions A category A consists of a Set of Types and a set of functions (or morphism) that connect the types Some properties of categories Every object has an identity function f: A => A Not all object have to be connect, i.e. take the identity category all objects only have arrows to themselves f: A => A, g: B => B Functions are compassable and composition is associative: f: A => B, g: B => C, h: C => D h(g(f(a))) === h(g)(f(a)) (f * g) * h === f * (g * h)