Category

A category in Category Theory is: ^{1 2}

• A collection of objects and morphisms that go from one object to another.
• There is a way to compose two morphisms into a third one which gives the result of applying the morphisms successively in an associative way.
• Each object has to have the identity morphism.

The identity morphism is useful, because it can be used as an argument to or a return from a higher-order function. Higher-order functions make the symbolic manipulation of functions possible. ²