Category Theory & The Yoneda Lemma 🧮

As I understand it (which isn’t very well), the branch of mathematics called Category Theory fundamentally shifts from looking at objects themselves, to looking at the relationships between objects. They've got this thing called “The Yoneda Lemma”, which essentially uses logic to prove the idea "you can define a thing by its relationships (rather than having to define it by its parts)". Being "proven" means we can build upon it as a strong foundation and do really cool things that we couldn't do before.

It sounds abstract because it is; but I see it as making the same fundamental shift as relatefulness: We shift from looking at ourselves as the fundamental unit of inquiry to looking at the relationships between ourselves. Changing the default perspective we're looking from, new stuff emerges. We recognize that we’re defined as much by our relationships with others—friends, coworkers, family—as we are by our self-authorship. We can keep going: Our relationships can be seen as objects, which can then be described by the relationships that make them up!

With love, Jordan