@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
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Functor Fact retweeted
Mathieu
@miniapeurOct 14
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Algebra Etc.@AlgebraFactOct 12
Categorical models of logics johndcook.com/blog/2026/10/1…
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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
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Matti Palli
@tritloSep 26
Lasagna is a monoid. Stack two lasagnas, you get one tall lasagna. This is in contrast to e.g. a pizza. Stacking two pizzas does not make a new pizza, the top pizza merely becomes a topping of the bottom pizza Follow me for more categorical insights
Daniel 🦔
@DanielW_KiwiSep 26
Visual monad explanation
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Anthony Bonato
@Anthony_BonatoSep 5
“Yes, but is it art?”
Art by Bernar Venet

ALT Art by Bernar Venet

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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! 🔗👇
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Hamzé 🦀
@HamzemlMay 3
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.
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Jonathan Gorard
@getjonwithitApr 5
Alexander Grothendieck My name is Alexander Grothendieck And Alfred Tarski’s "≅" is far too weak But just you wait Just you wait
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Math Files
@Math_files24 Dec 2025
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Mathieu
@miniapeur22 Dec 2025
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"Why I never learned category theory" Chapter 1, Exercise 1: Show the following diagram commutes
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"This follows from general theory, the details are in Lurie" "No they aren't, did you even read it?" "No, did you?" "No"
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Mathieu
@miniapeur14 Jul 2025
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(Weak) Homotopy Equivalences bartoszmilewski.com/2025/06/…

(Weak) Homotopy Equivalences

Previously: Fibrations and Cofibrations. In topology, we say that two shapes are the same if there is a homeomorphism– an invertible continuous map– between them. Continuity means that …

bartoszmilewski.com
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"There are two kinds of generalizations. One is cheap and the other is valuable. It is easy to generalize by diluting a little idea with a big terminology. It is much more difficult to prepare a refined and condensed extract from several good ingredients." -- George Pólya
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For a monoid M, TFAE: (1) The associativity diagram M × M × M → M × M ↓ ↓ M × M → M is a pull-back (of sets). (2) M is a group.
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I think it commutes
From https://arxiv.org/pdf/2505.00682

ALT From https://arxiv.org/pdf/2505.00682

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New post: 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

johndcook.com
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Stonean spaces, projective objects, the Riesz representation theorem, and (possibly) condensed mathematics terrytao.wordpress.com/2025/…

Stonean spaces, projective objects, the Riesz representation theorem, and (possibly) condensed ma...

A basic type of problem that occurs throughout mathematics is the lifting problem: given some space $latex {X}&fg=000000$ that “sits above” some other “base” space $late…

terrytao.wordpress.com
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