@FunctorFact

Functional programming and category theory tweets from @JohnDCook

 Houston, TX
johndcook.com/blog/applied-category-theory/
Joined June 2016
  • Tweets4.2K
  • Following6
  • Followers26.6K
212Media
The groups in the category of groups are the Abelian groups!
6
1
45
1,570
A group 'in a category' is not the same thing as the category of groups. You can have groups in any category that has products.
1
7
20
1,440
In the category of groups, direct products are products, free products are coproducts.
1
2
19
859
Interesting categories are big johndcook.com/blog/2025/12/2…

Interesting categories are big

You can most ignore matters of cardinality when using category theory, and yet there is a theorem that says category theory would be trivial without such issues.

johndcook.com
24
1,698
Hy: A Lisp that transforms to the Python abstract syntax tree docs.hylang.org/
1
3
1,917
'Theorems for Free' and related papers by Philip Wadler homepages.inf.ed.ac.uk/wadle…
8
2
25
2,015
'Coconut is a simple, elegant, Pythonic functional programming language that compiles to Python.' coconut-lang.org/
1
4
23
2,211
Functor Fact retweeted
Mathieu
@miniapeurOct 14
14
47
8
473
7,297
Epic and monic johndcook.com/blog/2018/08/2…

Epimorphisms and monomorphisms in category theory

Monic and epic are the category theory analogs of injective (one-to-one) and surjective (onto). Sometimes the correspondence is trivial, but sometimes not.

johndcook.com
1
13
905
A functor between two categories maps objects to objects and morphisms to morphisms in a structure-preserving way.
1
9
1
39
2,127
'This may be one of the gentlest introductions to the idea of categories and monads that you will find.' cdsmith.wordpress.com/2012/0…

Why Do Monads Matter?

(A Side Note: I’ve been formulating the final thoughts on this post for about a week now. In an entirely unrelated coincidence, a good friend of mine and fellow Haskell programmer, Doug Beard…

cdsmith.wordpress.com
9
51
2,843
Functor Fact retweeted
Algebra Etc.@AlgebraFactOct 12
Categorical models of logics johndcook.com/blog/2026/10/1…
4
35
2
257
9,660
Functor Fact retweeted
Louis Maddox@permutansOct 10
📄 Spivak (2026) Compositional Dynamics in Learning and Mechanics arxiv.org/abs/2606.28984

Compositional Dynamics in Learning and Mechanics

We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics. The syntax is an operad Arr whose objects are input-output...

arxiv.org
4
16
1
129
8,831
starring Denzel Washington
4
31
2,705
Don't fear the monad youtu.be/ZhuHCtR3xq8 by @lorentzframe

Brian Beckman: Don't fear the Monad

Cross posted from msdn's channel 9.Functional programming is incr...

youtube.com
2
15
1,556
The 'range' of a function f: A -> B is ambiguous. Some use the term to mean the codomain B and others to mean the image f(A).
1
24
1,819
A general theory of sub-things johndcook.com/blog/2022/01/2…

A general theory of sub-things | subobjects

A general theory of how to define one thing to be a subthing of another: subgroups, subspaces, subfields, etc.

johndcook.com
2
22
1,525
'Category theory has been called 'abstract nonsense' both by its friends and its detractors.' -- Joseph Goguen
3
6
1
32
1,532
Co-limits in category theory are also called direct limits, inductive limits, and right roots.
1
3
27
1,554
Limits in category theory are also called inverse limits, projective limits, and left roots.
1
7
2
26
3,125
Load more