Contents
An emerging branch of metamathematics dealing with mappings between things.
The idea of studying relationships rather than intrinsic characteristics matches a major advance in modern mathematics, the development of my research field, category theory. (Eugenia Cheng, x + y: A Mathematician’s Manifesto for Rethinking Gender)
This focus on relationships over elements echoes the insights of systems thinking, that the relationships between elements in a system are equally if not more relevant to the behavior of the system than the properties of the elements themselves. Indeed, the Stanford Encyclopedia of Philosophy describes category theory as “a general mathematical theory of structures and of systems of structures.”
Relationship to Programming
The mathematical concept of a category is akin to a “type” or “function” in programming, especially functional programming. Bartosz Milewski’s “Category Theory for Programmers” blog series examines in great detail what category theory has to teach functional programmers (also available as a YouTube series).