#category-theory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #category-theory, aggregated by home.social.
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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
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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
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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
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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
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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
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what's a good introductory video talk or text on coinduction and coinductive data types?
#typetheory #categorytheory #algebra #math #theoreticalComputerScience #recursion #FunctionalProgramming #coinduction
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"A monad is a monoid in the category of endofunctors" But what does that actually mean?
Let's use Haskell to discover it! -
"A monad is a monoid in the category of endofunctors" But what does that actually mean?
Let's use Haskell to discover it! -
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
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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
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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
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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/
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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/
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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/
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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/
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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/
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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.
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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.
-
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.
-
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.
-
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.
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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!
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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!
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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!
-
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!
-
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!
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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.
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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.
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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.
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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.
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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.
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Cool writeup presenting universal properties as natural isomorphisms:
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Cool writeup presenting universal properties as natural isomorphisms:
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Cool writeup presenting universal properties as natural isomorphisms:
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Cool writeup presenting universal properties as natural isomorphisms:
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Cool writeup presenting universal properties as natural isomorphisms:
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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🤦♂️ 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 -
🤦♂️ 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 -
🤦♂️ 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 -
📚🤖 "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 -
📚🤖 "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
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Building ML framework with Rust and Category Theory
https://hghalebi.github.io/category_theory_transformer_rs/
#HackerNews #ML #Rust #CategoryTheory #Framework #Development
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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