found my password #categorytheory #math

Tell me who your friends are and I'll tell you who you are. Picture a forest with a meadow, a rose garden, a mountain and a waterfall. We can draw arrows to show that there exists a path between each of these locations. We've created what in maths is called a category, since we have objects, the locations, and ways to get between them. In category theory, these paths are called morphisms. If you start at the meadow and want to get to the waterfall, you can either go straight there or you could go via the rose garden. It doesn't matter because in both cases you end up at the waterfall. Another seemingly unrelated category is the different translations of a book. Even though they describe different things, these two categories have the same structure. They are isomorphic and studying the structure of one can help us understand the other, or even other wildly different topics like quantum mechanics, algebra and linguistics.