Functor Fact

Haskell is not category theory pema.dev/2023/02/01/has…

If you've been struggling learning category theory, you might want to check out Paolo Perrone's 'Notes on Category theory: with examples from basic mathematics' available publicly on arXiv. These notes were produced during a class given to a diverse set of scientists (including chemists and physicists), with knowledge in linear algebra being the only subject assumed to be known! 🔗👇

'A comathematician is a device for turning cotheorems into ffee.'

Simply typed lambda calculus is the internal language of Cartesian closed categories (CCCs).

Given categories C and D, D^C is the category whose objects are functors from C to D and whose morphisms are natural transformations.

Simple example of Kleisli composition johndcook.com/blog/2022/11/1…

The mythology of category theory johndcook.com/blog/2026/05/0…

There are several things that have similar notation: the set Hom(A, B), the function Hom(A, g), and the functor Hom(A, -).

“As we now know, nobody truly understands macros.” -- Doug Hoyte, Let Over Lambda

Galois connections and Galois theory johndcook.com/blog/2022/07/2…

Python made AI accessible. Rust can make parts of AI understandable. That’s the bet behind Category Theory for Tiny ML in Rust. We’re building tiny ML systems from first principles using: Rust types typed transformations composition training loops category theory as an engineering tool Not abstraction cosplay. Executable structure. Working draft. Public feedback welcome.

Categorical databases categoricaldata.net

Category theory turns math inside-out: Definitions depend on nothing inside, but on everything outside.

The glass disk game (homological algebra) johndcook.com/blog/2025/03/2…

Haskell-Java interop blog.tweag.io/posts/2016-10-…

'Roughly speaking, homological algebra is concerned with the question of how much modules differ from being projective, injective, or flat.' -- M. Scott Osborne

Algebra : Strucure :: Coalgebra : Behavior

Categorical data analysis johndcook.com/blog/2018/04/1…

“It should be observed first that the whole concept of a category is essentially an auxiliary one; our basic concepts are essentially those of a functor and of a natural transformation.” — S. Eilenberg and S. Mac Lane

Universal properties are a fairly big conceptual hurdle to get over. But they all have the same flavor: there exists an object and a morphism such that everything factors uniquely through that object.