An overview of Category Theory. Back to Article
Back to Article

An overview of Category Theory. Public Domain

Public Domain

Public Domain

In category theory, a category is defined as having objects, arrows or morphisms, a way to compose arrows associatively, and an identity arrow.

Objects are the smallest discrete units of a category; in Higher Category Theory objects are zero-morphisms.

Arrows indicate a change from one object to another object; in Higher Category Theory arrows are one-morphisms. The arrow the object points from is often referred to as the source, and the object the arrow points to is often referred to as the target.

Identity arrows point from source to source, and both the source and target are the exact same. Common maths examples are adding zero, subtracting zero, multiplying by one, and dividing by one.

Composition funnels an applied function into another. In mathematics this is written: h( g( f( x ) ) ), function h applied to function g applied to function f applied to value x. In category theory composition is written: h*g*f. ( where * is an open dot )

Associativity means composed functions or operations can be evaluated in any order, h*(g*f)=(h*g)*f.