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#categorytheory

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Jencel Panic<p>A <a href="https://mathstodon.xyz/tags/monad" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>monad</span></a> is when you know how to convert $M (M a)$ to $M a$, but not $M a$ to $a$.</p><p><a href="https://mathstodon.xyz/tags/haskell" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>haskell</span></a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> <a href="https://mathstodon.xyz/tags/functionalprogramming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>functionalprogramming</span></a></p>
2something<p><span>The set of all sets that are not big enough to trigger Russell's Paradox.<br><br><br>Okay that sounds like a joke, but I have a clear memory of my algebra professor in undergrad saying "If you have a large category, you can always shrink it to a small category that includes all the objects you care about."<br><br>Unless you're a foundations creature, in which case the objects you care about might include sets or categories which are big enough to cause trouble.<br><br></span><a href="https://transfem.social/tags/SetTheory" rel="nofollow noopener noreferrer" target="_blank">#SetTheory</a> <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener noreferrer" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/Math" rel="nofollow noopener noreferrer" target="_blank">#Math</a></p>
2something<p><span>The GNU project claims their software is "free," but I have never seen a proof that GNU Sed is a free object in the category of software.<br><br></span><a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener noreferrer" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/GNU" rel="nofollow noopener noreferrer" target="_blank">#GNU</a></p>
Tom de Jong<p>Many thanks to everyone who attended and made this an amazing day of <a href="https://mathstodon.xyz/tags/logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>logic</span></a>, <a href="https://mathstodon.xyz/tags/computabilitytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>computabilitytheory</span></a> and <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a>!</p><p>Recordings and slides will be available on the website sometime next week (hopefully)!</p>
Manuel Baltieri<p>2025 is looking like a great year for work at the intersection of <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a>, <a href="https://mathstodon.xyz/tags/systemstheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>systemstheory</span></a> and <a href="https://mathstodon.xyz/tags/probabilitytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>probabilitytheory</span></a>, this thread will be a very biased collection of works I'm hoping to read as soon as possible!</p><p>Starting with:<br>"Logical Aspects of Virtual Double Categories"<br><a href="https://mastoxiv.page/@arXiv_mathCT_bot/113921693949589956" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">mastoxiv.page/@arXiv_mathCT_bo</span><span class="invisible">t/113921693949589956</span></a></p>
José A. Alonso<p>Readings shared February 24, 2025. <a href="https://jaalonso.github.io/vestigium/posts/2025/02/24-readings_shared_02-24-25" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">jaalonso.github.io/vestigium/p</span><span class="invisible">osts/2025/02/24-readings_shared_02-24-25</span></a> <a href="https://mathstodon.xyz/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AI</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Clojure" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Clojure</span></a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FunctionalProgramming</span></a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Haskell</span></a> <a href="https://mathstodon.xyz/tags/ITP" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ITP</span></a> <a href="https://mathstodon.xyz/tags/LLMs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LLMs</span></a> <a href="https://mathstodon.xyz/tags/LeanProver" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LeanProver</span></a> <a href="https://mathstodon.xyz/tags/Lisp" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Lisp</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Math</span></a></p>
Chris Grossack (she/they)<p>Here's a cute <a href="https://sunny.garden/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> <a href="https://sunny.garden/tags/puzzle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>puzzle</span></a>:</p><p>(1) Prove the forgetful functor from (ℤ-)graded vector spaces (with all linear maps) to vector spaces admits infinitely many distinct left adjoints.</p><p>(2) How do you square this with the fact that left adjoints are unique when they exist?</p>
Jencel Panic<p>Non-natural transformation example</p><p><a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> </p><p><a href="https://math.stackexchange.com/questions/2772832/non-natural-transformation-example/2772881#2772881" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">math.stackexchange.com/questio</span><span class="invisible">ns/2772832/non-natural-transformation-example/2772881#2772881</span></a></p>
Jencel Panic<p>I feel that we are just scratching the surface of what <a href="https://mathstodon.xyz/tags/programming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>programming</span></a> languages are, and even what reasoning is. Our current languages would look like morze code to future generations.</p><p>(No I am not referring to anything related to <a href="https://mathstodon.xyz/tags/ai" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ai</span></a> )</p><p>The keywords for this toot are <a href="https://mathstodon.xyz/tags/haskellcurry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>haskellcurry</span></a> <a href="https://mathstodon.xyz/tags/lambda" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>lambda</span></a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> etc.</p>
2something<p><span>The Category Theorists tell me there is no category of categories, but then what's this?<br></span><a href="https://www.mediawiki.org/wiki/Category:Category" rel="nofollow noopener noreferrer" target="_blank">https://www.mediawiki.org/wiki/Category:Category</a><span><br><br></span><a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener noreferrer" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/CategoryOfCategories" rel="nofollow noopener noreferrer" target="_blank">#CategoryOfCategories</a> <a href="https://transfem.social/tags/Wiki" rel="nofollow noopener noreferrer" target="_blank">#Wiki</a> <a href="https://transfem.social/tags/MediaWiki" rel="nofollow noopener noreferrer" target="_blank">#MediaWiki</a></p>
Ryan Ruff<p>Happy <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Caturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Caturday</span></a>! Regrettably, I couldn't find sufficient time for progress this week so things are being put on "paws" for a bit. Instead, I spent some time reflecting on the past 90 weeks of <a href="https://mathstodon.xyz/tags/cats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cats</span></a> and <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a>. <a href="https://rruff82.github.io/LS-Categories/interlude.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rruff82.github.io/LS-Categorie</span><span class="invisible">s/interlude.html</span></a></p>
Jencel Panic<p>If you need one more <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> <a href="https://mathstodon.xyz/tags/haskell" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>haskell</span></a> book, this one is good:<br><a href="https://github.com/jwbuurlage/category-theory-programmers" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">github.com/jwbuurlage/category</span><span class="invisible">-theory-programmers</span></a></p>
José A. Alonso<p>Category theory illustrated. ~ Jencel Panic. <a href="https://abuseofnotation.github.io/category-theory-illustrated/00_about/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">abuseofnotation.github.io/cate</span><span class="invisible">gory-theory-illustrated/00_about/</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a></p>
Ryan Ruff<p>Happy <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Caturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Caturday</span></a>! For <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> this week, I drew out some products and sums to get my bearings in the category of pointed sets. The <a href="https://mathstodon.xyz/tags/cats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cats</span></a> also did some exploring this week, so here's Alphonse surveying holiday festivities from a safe distance. <a href="https://rruff82.github.io/LS-Categories/session28-p2.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rruff82.github.io/LS-Categorie</span><span class="invisible">s/session28-p2.html</span></a></p>
ma𝕏pool<p>Shape, Symmetries, and Structure: The Changing Role of Mathematics in Machine Learning Research by Henry Kvinge<br><a href="https://thegradient.pub/shape-symmetry-structure/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">thegradient.pub/shape-symmetry</span><span class="invisible">-structure/</span></a></p><p>Maths and statistics struggle to provide immediate insight into the latest ML breakthroughs. The role of mathematics is evolving. It's use is shifting to higher-level such as matching architecture to underlying task structure or data symmetries.. </p><p>In other worlds, fiber your bundles. </p><p>Some recent papers from the author seem relevant to the essay: </p><p>Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classes <a href="https://arxiv.org/abs/2411.07467" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2411.07467</span><span class="invisible"></span></a></p><p>Machine Learning meets Algebraic Combinatorics: A Suite of Datasets to Accelerate AI for Mathematics Research<br><a href="https://openreview.net/pdf?id=KQ1gI5qzAf" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">openreview.net/pdf?id=KQ1gI5qz</span><span class="invisible">Af</span></a></p><p>What Makes a Machine Learning Task a Good Candidate<br>for an Equivariant Network<br><a href="https://openreview.net/pdf?id=46vfUIfIo1" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">openreview.net/pdf?id=46vfUIfI</span><span class="invisible">o1</span></a></p><p><a href="https://mathstodon.xyz/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ML</span></a> <a href="https://mathstodon.xyz/tags/MachineLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MachineLearning</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a><br><a href="https://mathstodon.xyz/tags/categoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categoryTheory</span></a></p>
José A. Alonso<p>Category theory using Haskell (An introduction with Moggi and Yoneda). ~ Shuichi Yukita. <a href="https://link.springer.com/book/10.1007/978-3-031-68538-5" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">link.springer.com/book/10.1007</span><span class="invisible">/978-3-031-68538-5</span></a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Haskell</span></a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FunctionalProgramming</span></a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a></p>
Ryan Ruff<p>Happy <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Caturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Caturday</span></a>! This week in <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a>, I finally finished up L&amp;S Session 27. There's a lot I don't understand still, but moving on seems like the course to take. Meanwhile, the <a href="https://mathstodon.xyz/tags/cats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cats</span></a> enjoyed a little kitty couch party -- but with some personal space. <a href="https://rruff82.github.io/LS-Categories/session27-p17.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rruff82.github.io/LS-Categorie</span><span class="invisible">s/session27-p17.html</span></a></p>
Marco Paviotti<p>Dear all, </p><p>I am looking for a <a href="https://mathstodon.xyz/tags/PhD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PhD</span></a> student to work on (any subset of) these topics: <br><a href="https://mathstodon.xyz/tags/semantics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>semantics</span></a>, <a href="https://mathstodon.xyz/tags/domaintheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>domaintheory</span></a>, <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>categorytheory</span></a> <a href="https://mathstodon.xyz/tags/typetheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>typetheory</span></a> and <a href="https://mathstodon.xyz/tags/functional" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>functional</span></a> programming. </p><p>Deadline for application is 15th of February 2025.</p><p>Please get in touch if interested, here's the official call: <a href="https://www.kent.ac.uk/scholarships/search/FN15COMPGR01" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">kent.ac.uk/scholarships/search</span><span class="invisible">/FN15COMPGR01</span></a></p>
Ryan Ruff<p>It's <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Caturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Caturday</span></a>! Time for more <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> and <a href="https://mathstodon.xyz/tags/cats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cats</span></a>! Everybody is glad to be home! Alphonse definitely missed his heated blanket! I managed to make it through "part" of an exercise in L&amp;S and brainstormed some ideas on how to keep moving forward. <a href="https://rruff82.github.io/LS-Categories/session27-p16.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rruff82.github.io/LS-Categorie</span><span class="invisible">s/session27-p16.html</span></a></p>
Ryan Ruff<p>Happy <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CategoryTheory</span></a> <a href="https://mathstodon.xyz/tags/Caturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Caturday</span></a>! This week in <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a>, I tried to make headway on the last exercise in L&amp;S Session 27 by exploring simple examples. The <a href="https://mathstodon.xyz/tags/cats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cats</span></a> came with us for the holiday. They were scared at first, but soon learned the bed at grandma's is comfy! <a href="https://rruff82.github.io/LS-Categories/session27-p15.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">rruff82.github.io/LS-Categorie</span><span class="invisible">s/session27-p15.html</span></a></p>
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