Category Theory is a subfield of pure mathematics studying any structure that contains objects and their relations (referred to as morphisms). It emerged in the study of algebraic topology, then went on to apply beyond mathematics and into various scientific disciplines, a metamathematical framework comparable to that of type theory and set theory. The notion of compositionality is what differs category theory from graph theory, in which the nodes themselves can be categories.

Current research on applied category theory and Categories for AI are useful and relevant for topics close to LW, such as Rationality, AI Safety, and Game theory. Due to its abstract nature, category theory is jokingly criticized as being "abstract nonsense". A major theorem result is Yoneda embedding, which is basically the idea that an object can be defined by its all of its relations.