#categorytheory — Public Fediverse posts

One of the miraculous proofs truly foundational of #categoryTheory - the proof that product (and any other object that is defined using universal property) is unique up to a (unique) isomorphism.

I have to remember to include it in #categorytheoryillustrated

https://proofwiki.org/wiki/Product_%28Category_Theory%29_is_Unique

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

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

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

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

🤦‍♂️ 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

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

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

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

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

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

• Logic Syllabus
• Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

I've been on a longer hiatus from livestreaming than I originally intended, but you can see me give a seminar talk this evening at the The New York City Category Theory Seminar:

https://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.html

I'll be talking about the invariant theory part of my thesis (https://arxiv.org/abs/2402.18063) at 7PM, New York time. I'll discuss how I found that every (positive) property of finite structures can be checked by counting small* substructures.

*Terms and conditions may apply. Small is constrained by the logical complexity of a property and may not conform to mundane notions of smallness in bad cases.

#CategoryTheory #combinatorics #logic #Bourbaki #algebra #AbstractAlgebra

I have a new(ish) preprint on the arXiv! You can find "Invariants of structures" at https://arxiv.org/abs/2402.18063. This is a somewhat embellished version of one half of my PhD thesis. A talk which I gave about this subject in the fall of 2022 is available at https://www.youtube.com/watch?v=5TeGZZ_mepc.

In this new version, I have finally added an explicit description of something I've been telling people for years: My main result shows that any first-order property of finite structures can be computed by counting small substructures. Perhaps surprisingly, this comes as a result of synthesizing a categorical treatment of Bourbaki's notion of mathematical structure with Hilbert's classical result on symmetric polynomials.

#CategoryTheory #combinatorics #algebra #AbstractAlgebra #logic #Bourbaki

Realising that without a recommendation engine posts can't get anywhere without hashtags, lemme add a bunch now: #categorytheory #Python #diagram #monoidal #GraphicalFormalism #PicturingQuantum #GraphicalLinearAlgebra #LogicalNAND
#CharlesSandersPeirce

Just posted this talk (https://youtu.be/5TeGZZ_mepc) I gave on the categorified invariant theory part of my PhD thesis last fall! You can also find my thesis itself online now at https://aten.cool/documents/thesis.pdf if you'd like to see more.

Part of the reason I waited so long to post this is because I kind of flubbed the last example after the main part of the talk due to having not looked at this stuff for a while before giving the lecture. I thought I'd cut that last part out once I had more time, but enough time has passed and it no longer bothers me.

I actually wrote most of this part of my thesis in 2020, so I waited a long time to advertise this work.

#math #thesis #algebra #AbstractAlgebra #CategoryTheory #Bourbaki #combinatorics