Category: Category theory

Category theory for data science: cautious optimism

I’m cautiously optimistic about applications of category theory. I believe category theory has the potential to be useful, but I’m skeptical of most claims to have found useful applications. Category theory has found useful application, especially behind the scenes, but a lot of supposed applications remind me of a line from Colin McLarty: [Jean-Pierre] Serre […]

How category theory is applied

Instead of asking whether an area of mathematics can be applied, it’s more useful to as how it can be applied. Differential equations are directly and commonly applied. Ask yourself what laws govern the motion of some system, write down these laws as differential equations, then solve them. Statistical models are similarly direct: propose a […]

Groups in categories

The first time I saw a reference to a “group in a category” I misread it as something in the category of groups. But that’s not what it means. Due to an unfortunately choice of terminology, “in” is more subtle than just membership in a class. This is related to another potentially misleading term, algebraic […]

Monads and generalized elements

Paolo Perrone gives a nice, succinct motivation for monads in the introduction to his article on probability and monads. … a monad is like a consistent way of extending spaces to include generalized elements of a specific kind. He develops this idea briefly, and links to his dissertation where he gives a longer exposition (pages […]