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Functor Fact @FunctorFact

Functional programming and category theory tweets from @JohnDCook

Joined June 2016
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'Interconnectedness makes big programs eventually crumble under their own weight.' -- Simon Peyton Jones
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The Zen of Stateless State - The State Monad youtu.be/XxzzJiXHOJs by @lorentzframe

Brian Beckman: The Zen of Stateless State - The State Monad

Concurrency is a problem that faces all developers as we move to th...

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Enriched categories johndcook.com/blog/2023/10/0…

Enriched categories

When the set of functions between two objects has more structure than just a set, we say the category the objects come from is enriched

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Universal coalgebra: a theory of systems sciencedirect.com/science/ar…
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The symbol ⊣ as in F ⊣ G if F is a left adjoint for G, is U 22A3 in Unicode, \dashv in LaTeX. Right adjoint ⊢ is U_22A2, \vdash.
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ODE solver as a fold johndcook.com/blog/2016/06/0…

Runge-Kutta implemented as a fold in Haskell

An ordinary differential equation solver like the famous Runge Kutta method is naturally expressed as a fold in functional programming.

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'General category theory springs no nasty surprises: any sensible equation you can write down is true.' -- Tom Leinster
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Haskell Programming from First Principles haskellbook.com/

Haskell Programming

An exercise-driven Haskell book for beginners that works for non-programmers and experienced hackers alike.

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'Lisp's core occupies some sort of optimum in the space of programming languages.' -- John McCarthy
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A terminal object is a limit over an empty diagram.
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Adjunctions johndcook.com/blog/2025/04/2…

Adjoints in linear algebra and category theory

Using the notion of adjoint in linear algebra as a motivation for the notion of adjoint in category theory. Metaphors for adjoints

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Typed Clojure: An optional type system for Clojure typedclojure.org/
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Create commutative diagrams with TikZ ctan.org/pkg/tikz-cd
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F# resources fsharp.org/learn.html
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Incanter: a Clojure-based, R-like platform for statistical computing and graphics incanter.org/
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Natural transformations johndcook.com/blog/2017/03/1…

Category theory: Natural transformation

Category theory was developed to formalize what it means for something to be "natural." The solution was natural transformations.

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Intersections, inverse images, kernels, and products can all be formulated as pullbacks.
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The category of fields has no initial or terminal objects.
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Category theory without categories johndcook.com/blog/2023/05/2…

Category theory without categories

Isolating one of the difficult aspects of category theory by considering it separately in a more concrete context.

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