#categorytheory — Public Fediverse posts

what's a good introductory video talk or text on coinduction and coinductive data types?

#typetheory #categorytheory #algebra #math #theoreticalComputerScience #recursion #FunctionalProgramming #coinduction

New paper: "Valuation Without ℝ: A Category-Theoretic Foundation for Finite Measurement"

Can measurement be formalized independently of real numbers AND set theory?

We axiomatize "valuation" as a graded distinguishability map satisfying the ultrametric inequality. Dimension emerges as the growth exponent of the distinguishability graph.

Full paper: https://doi.org/10.5281/zenodo.21795656

#pAdic #QuantumFoundations #CategoryTheory #Measurement

A final monad theory blog post in the current series about transferring nice properties of monads along strong monad morphisms. Today, quotients:

https://stringdiagram.com/2026/08/07/quotients-of-commutative-affine-and-relevant-monads/

#categorytheory

A final monad theory blog post in the current series about transferring nice properties of monads along strong monad morphisms. Today, quotients:

https://stringdiagram.com/2026/08/07/quotients-of-commutative-affine-and-relevant-monads/

#categorytheory

Just a reminder, if you are about to take a category theory course next term/semester.

There is a page of links to reasonably accessible and (legally!) freely downloadable lecture notes etc. at https://logicmatters.net/categories. You could very well find there some helpful preliminary/parallel reading at a level that suits you.

At the gentler end, there are my own notes *Introducing Category Theory*, freely downloadable of course but also available as a minimum cost paperback. Some students do like the book!

If you giving a category theory course, please do alert your students to the links page https://logicmatters.net/categories -- they may well find it useful.

#CategoryTheory

Just a reminder, if you are about to take a category theory course next term/semester.

There is a page of links to reasonably accessible and (legally!) freely downloadable lecture notes etc. at https://logicmatters.net/categories. You could very well find there some helpful preliminary/parallel reading at a level that suits you.

At the gentler end, there are my own notes *Introducing Category Theory*, freely downloadable of course but also available as a minimum cost paperback. Some students do like the book!

If you giving a category theory course, please do alert your students to the links page https://logicmatters.net/categories -- they may well find it useful.

#CategoryTheory

Just learnt that our paper "A study of Kock's fat Delta" (https://arxiv.org/abs/2503.10963) with Nicolai Kraus (@Nicolai_Kraus), Simona Paoli and Stiéphen Pradal (@Stiephen) was accepted for publication in the Journal of Pure and Applied Algebra (JPAA).

I'm quite happy about this, but I'm especially pleased for Stiéphen who's currently working hard to write up his PhD thesis!

#categorytheory

Just learnt that our paper "A study of Kock's fat Delta" (https://arxiv.org/abs/2503.10963) with Nicolai Kraus (@Nicolai_Kraus), Simona Paoli and Stiéphen Pradal (@Stiephen) was accepted for publication in the Journal of Pure and Applied Algebra (JPAA).

I'm quite happy about this, but I'm especially pleased for Stiéphen who's currently working hard to write up his PhD thesis!

#categorytheory

While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.

#math #mathematics #topology #algebra #CategoryTheory

While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.

#math #mathematics #topology #algebra #CategoryTheory

Cool writeup presenting universal properties as natural isomorphisms:

https://math.stackexchange.com/questions/3688510/understanding-universal-property-and-universal-element-from-category-theory-in

#categoryTheory

Cool writeup presenting universal properties as natural isomorphisms:

https://math.stackexchange.com/questions/3688510/understanding-universal-property-and-universal-element-from-category-theory-in

#categoryTheory

Random #categoryTheory fact: The Yoneda lemma can be seen (among 1000 other things) as a generalization of the definition that a set contains no structure, other than its elements.

Random #categoryTheory fact: The Yoneda lemma can be seen (among 1000 other things) as a generalization of the definition that a set contains no structure, other than its elements.

Does anybody know how to typeset pullback/pushout corners in typst/fletcher?
The code provided at https://github.com/Jollywatt/typst-fletcher/issues/50#issuecomment-2851846670 does not quite work for me and even when it does, it requires experimenting with degrees which is bad.

[Update] I added my own workaround as a reply to the GitHub issue.

#typst #typesetting #categorytheory

Does anybody know how to typeset pullback/pushout corners in typst/fletcher?
The code provided at https://github.com/Jollywatt/typst-fletcher/issues/50#issuecomment-2851846670 does not quite work for me and even when it does, it requires experimenting with degrees which is bad.

[Update] I added my own workaround as a reply to the GitHub issue.

#typst #typesetting #categorytheory

🤦‍♂️ Ah yes, because what every overworked developer dreams of is an IDE that speaks the fluent gibberish of category theory. 🚀 Just sprinkle some "categorical magic dust" on your databases and watch them transform (or maybe just disappear into the void). Call Conexus AI for a personalized headache consultation. 📞🤯
https://categoricaldata.net/ #overworkeddevelopers #categorytheory #IDEs #ConexusAI #techhumor #HackerNews #ngated

🤦‍♂️ Ah yes, because what every overworked developer dreams of is an IDE that speaks the fluent gibberish of category theory. 🚀 Just sprinkle some "categorical magic dust" on your databases and watch them transform (or maybe just disappear into the void). Call Conexus AI for a personalized headache consultation. 📞🤯
https://categoricaldata.net/ #overworkeddevelopers #categorytheory #IDEs #ConexusAI #techhumor #HackerNews #ngated

📚🤖 "Behold! The magnum opus on #Rust and Category Theory that's sure to revolutionize your understanding of... nothing. 😂 Dive into this unfinished 'draft' if you're into the esoteric joy of turning simple concepts into convoluted gibberish. 🚀👨‍💻✨"
https://hghalebi.github.io/category_theory_transformer_rs/ #CategoryTheory #EsotericHumor #TechHumor #Programming #HackerNews #ngated

📚🤖 "Behold! The magnum opus on #Rust and Category Theory that's sure to revolutionize your understanding of... nothing. 😂 Dive into this unfinished 'draft' if you're into the esoteric joy of turning simple concepts into convoluted gibberish. 🚀👨‍💻✨"
https://hghalebi.github.io/category_theory_transformer_rs/ #CategoryTheory #EsotericHumor #TechHumor #Programming #HackerNews #ngated

Building ML framework with Rust and Category Theory

https://hghalebi.github.io/category_theory_transformer_rs/

#HackerNews #ML #Rust #CategoryTheory #Framework #Development

Building ML framework with Rust and Category Theory

https://hghalebi.github.io/category_theory_transformer_rs/

#HackerNews #ML #Rust #CategoryTheory #Framework #Development

Towards a Higher-Order Bialgebraic Denotational Semantics by Sergey Goncharov, @[email protected], @[email protected], Henning Urbat, and me has been (unconditionally) accepted at ICFP'26! Abstract below ​:Blobhaj_Read_Octopus:​

#icfp #functionalProgramming #programmingLanguages #semantics #coalgebra #categoryTheory

Towards a Higher-Order Bialgebraic Denotational Semantics by Sergey Goncharov, @[email protected], @[email protected], Henning Urbat, and me has been (unconditionally) accepted at ICFP'26! Abstract below ​:Blobhaj_Read_Octopus:​

#icfp #functionalProgramming #programmingLanguages #semantics #coalgebra #categoryTheory

From 11:00 to 12:00 on Thursday, April 30, the PLUSLE reading group will discuss "Abstract Syntax and Variable Binding" by Marcelo Fiore, Gordon Plotkin, and Daniele Turi.

https://plsl.acp.sdu.dk/posts/2026-04-30-abstract-syntax-and-variable-binding/

#PLUSLE #syntax #programmingLanguages #categoryTheory #lambdaCalculus

Oh joy, another attempt at 'explaining' Category Theory using #orders, because clearly the first thing we all need is more #abstraction in our lives. 🎉 In a groundbreaking revelation, the article tells us orders are about #relationships. 🤯 Who knew binary relations could be so riveting? 🙄
https://abuseofnotation.github.io/category-theory-illustrated/04_order/ #CategoryTheory #HackerNews #HackerNews #ngated

Oh joy, another attempt at 'explaining' Category Theory using #orders, because clearly the first thing we all need is more #abstraction in our lives. 🎉 In a groundbreaking revelation, the article tells us orders are about #relationships. 🤯 Who knew binary relations could be so riveting? 🙄
https://abuseofnotation.github.io/category-theory-illustrated/04_order/ #CategoryTheory #HackerNews #HackerNews #ngated

Category Theory Illustrated – Orders

https://abuseofnotation.github.io/category-theory-illustrated/04_order/

#HackerNews #CategoryTheory #Orders #Illustration #Math #Education #Programming

Category Theory Illustrated – Orders

https://abuseofnotation.github.io/category-theory-illustrated/04_order/

#HackerNews #CategoryTheory #Orders #Illustration #Math #Education #Programming

Someone should make one of those "top 10 most satisfying" videos but for #CategoryTheory diagram chasing proofs

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics ( #mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

Readings shared April 4, 2026. https://jaalonso.github.io/vestigium/posts/2026/04/04-readings_shared_04-04-26 #AI #AI4Math #ATP #Agda #AlphaProof #Autoformalization #CategoryTheory #CoqProver #FunctionalProgramming #ITP #IsabelleHOL #LLMs #LambdaCalculus #LeanProver #Lisp #Logic #LogicProgramming #LLMs #Math #Physics #Programming #Prolog #Racket #RocqProver #Vampire

Readings shared April 4, 2026. https://jaalonso.github.io/vestigium/posts/2026/04/04-readings_shared_04-04-26 #AI #AI4Math #ATP #Agda #AlphaProof #Autoformalization #CategoryTheory #CoqProver #FunctionalProgramming #ITP #IsabelleHOL #LLMs #LambdaCalculus #LeanProver #Lisp #Logic #LogicProgramming #LLMs #Math #Physics #Programming #Prolog #Racket #RocqProver #Vampire

Category theory illustrated: Types. ~ Jencel Panic. https://abuseofnotation.github.io/category-theory-illustrated/06_type/ #CategoryTheory #Math

Category theory illustrated: Types. ~ Jencel Panic. https://abuseofnotation.github.io/category-theory-illustrated/06_type/ #CategoryTheory #Math

What Category Theory Teaches Us About DataFrames

https://mchav.github.io/what-category-theory-teaches-us-about-dataframes/

#HackerNews #CategoryTheory #DataFrames #DataScience #Programming #HackerNews

What Category Theory Teaches Us About DataFrames

https://mchav.github.io/what-category-theory-teaches-us-about-dataframes/

#HackerNews #CategoryTheory #DataFrames #DataScience #Programming #HackerNews

Thanks to our speakers and @Stiephen all the slides for PSSL 112 are now available on the PSSL website! https://sites.google.com/view/pssl112/program

#CategoryTheory #Logic

Published a new chapter of #categorytheoryillustrated - Types

https://abuseofnotation.github.io/category-theory-illustrated/06_type/

#categorytheory #mathematics #haskell

Readings shared March 29, 2026. https://jaalonso.github.io/vestigium/posts/2026/03/30-readings_shared_02-29-26 #AI #AI4Math #CategoryTheory #ITP #LeanProver #Logic #Math #Programming

Formally verifying digital circuits with category theory in Lean. ~ Matt Hunzinger. https://matt.hunzinger.me/2026/03/28/circuits.html #LeanProver #ITP #CategoryTheory

RE: https://fosstodon.org/@zurihac/116040336310097135

Come meet me there!

#categorytheory #haskell

Question for people with background in #categorytheory , which of the two is more correct/understandable:

"A monoid is...

#categorytheoryillustrated

Readings shared March 09, 2026. https://jaalonso.github.io/vestigium/posts/2026/03/10-readings_shared_02-09-26 #AI #AI4Math #CategoryTheory #CoqProver #Emacs #FunctionalProgramming #Haskell #ITP #IsabelleHOL #LambdaCalculus #LeanProver #Lisp #Math #Physics #RocqProver

Can the most abstract math make the world a better place? ~ Natalie Wolchover https://www.quantamagazine.org/can-the-most-abstract-math-make-the-world-a-better-place-20260304/ #CategoryTheory #Math