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José A. AlonsoReadings shared July 4, 2025. <a href="https://jaalonso.github.io/vestigium/posts/2025/07/05-readings_shared_07-04-25" rel="nofollow noopener" translate="no" target="_blank">https://jaalonso.github.io/vestigium/posts/2025/07/05-readings_shared_07-04-25</a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#FunctionalProgramming</a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#Haskell</a> <a href="https://mathstodon.xyz/tags/ITP" class="mention hashtag" rel="nofollow noopener" target="_blank">#ITP</a> <a href="https://mathstodon.xyz/tags/IsabelleHOL" class="mention hashtag" rel="nofollow noopener" target="_blank">#IsabelleHOL</a> <a href="https://mathstodon.xyz/tags/LLMs" class="mention hashtag" rel="nofollow noopener" target="_blank">#LLMs</a> <a href="https://mathstodon.xyz/tags/LeanProver" class="mention hashtag" rel="nofollow noopener" target="_blank">#LeanProver</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Rust" class="mention hashtag" rel="nofollow noopener" target="_blank">#Rust</a> <a href="https://mathstodon.xyz/tags/TypeTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#TypeTheory</a>

Counting Is Hard<a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

ThomasRobert Rosen's approach of grounding formalization in science in the ultimate formalization, math, is as self-similar as thinking about thought.His use of "category theory" provides a mathematical analogy to analogies.I must confess that I need a lot of time to understand his writings - I keep learning new things every time I read it again.<a href="https://mas.to/tags/RobertRosen" class="mention hashtag" rel="nofollow noopener" target="_blank">#RobertRosen</a> <a href="https://mas.to/tags/Formalization" class="mention hashtag" rel="nofollow noopener" target="_blank">#Formalization</a> <a href="https://mas.to/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

Counting Is HardAs promised. Here is the sequel to my Weihrauch reductions are Containers post, this time relating strong reductions to dependent adaptors. Enjoy!<a href="https://www.countingishard.org/blog/strong-reducibility-as-an-adaptor" rel="nofollow noopener" translate="no" target="_blank">https://www.countingishard.org/blog/strong-reducibility-as-an-adaptor</a><a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#computability</a>

Ramin Honary<a class="u-url mention" href="https://chaos.social/@das_g" rel="nofollow noopener" target="_blank">@das_g</a> True. It is certainly magical that there is a programming language which defines a state monad called “IO” (or sometimes “Effect”) which carries around with it a symbol of the entire Real World in order to model the idea that any evaluation of a function of that type of monad may (or may not) create a change somewhere out in the real world, as opposed to “pure” functions which can only ever manipulate the stack.<a class="hashtag" href="https://fe.disroot.org/tag/tech" rel="nofollow noopener" target="_blank">#tech</a> <a class="hashtag" href="https://fe.disroot.org/tag/software" rel="nofollow noopener" target="_blank">#software</a> <a class="hashtag" href="https://fe.disroot.org/tag/haskell" rel="nofollow noopener" target="_blank">#Haskell</a> <a class="hashtag" href="https://fe.disroot.org/tag/programminglanguage" rel="nofollow noopener" target="_blank">#ProgrammingLanguage</a> <a class="hashtag" href="https://fe.disroot.org/tag/typetheory" rel="nofollow noopener" target="_blank">#TypeTheory</a> <a class="hashtag" href="https://fe.disroot.org/tag/categorytheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a>

DarthViI've been reading "Category Theory Illustrated" by Jencel Panic (more about it here <a href="https://abuseofnotation.github.io/category-theory-illustrated/" rel="nofollow noopener" translate="no" target="_blank">https://abuseofnotation.github.io/category-theory-illustrated/</a>).I am reading about functors, but I wanted to share some screenshots about the Curry-Howard Isomorphism.<a href="https://hachyderm.io/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://hachyderm.io/tags/CurryHowardIsomorphism" class="mention hashtag" rel="nofollow noopener" target="_blank">#CurryHowardIsomorphism</a>

Jencel PanicA <a href="https://mathstodon.xyz/tags/monad" class="mention hashtag" rel="nofollow noopener" target="_blank">#monad</a> is when you know how to convert $M (M a)$ to $M a$, but not $M a$ to $a$.<a href="https://mathstodon.xyz/tags/haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#haskell</a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/functionalprogramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#functionalprogramming</a>

José A. AlonsoCategory theory using Haskell (An introduction with Moggi and Yoneda). ~ Shuichi Yukita. <a href="https://books.google.com/books?id=4Xc2EQAAQBAJ" rel="nofollow noopener" translate="no" target="_blank">https://books.google.com/books?id=4Xc2EQAAQBAJ</a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#Haskell</a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#FunctionalProgramming</a>

2somethingThe set of all sets that are not big enough to trigger Russell's Paradox. 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." 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. <a href="https://transfem.social/tags/SetTheory" rel="nofollow noopener" target="_blank">#SetTheory</a> <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/Math" rel="nofollow noopener" target="_blank">#Math</a>

2somethingThe 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. <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/GNU" rel="nofollow noopener" target="_blank">#GNU</a>

Chris Grossack (she/they)Here's a cute <a href="https://sunny.garden/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://sunny.garden/tags/puzzle" class="mention hashtag" rel="nofollow noopener" target="_blank">#puzzle</a>:(1) Prove the forgetful functor from (ℤ-)graded vector spaces (with all linear maps) to vector spaces admits infinitely many distinct left adjoints.(2) How do you square this with the fact that left adjoints are unique when they exist?

2somethingThe Category Theorists tell me there is no category of categories, but then what's this? <a href="https://www.mediawiki.org/wiki/Category:Category" rel="nofollow noopener" target="_blank">https://www.mediawiki.org/wiki/Category:Category</a> <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/CategoryOfCategories" rel="nofollow noopener" target="_blank">#CategoryOfCategories</a> <a href="https://transfem.social/tags/Wiki" rel="nofollow noopener" target="_blank">#Wiki</a> <a href="https://transfem.social/tags/MediaWiki" rel="nofollow noopener" target="_blank">#MediaWiki</a>

Marco PaviottiDear all, I am looking for a <a href="https://mathstodon.xyz/tags/PhD" class="mention hashtag" rel="nofollow noopener" target="_blank">#PhD</a> student to work on (any subset of) these topics: <a href="https://mathstodon.xyz/tags/semantics" class="mention hashtag" rel="nofollow noopener" target="_blank">#semantics</a>, <a href="https://mathstodon.xyz/tags/domaintheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#domaintheory</a>, <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/typetheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#typetheory</a> and <a href="https://mathstodon.xyz/tags/functional" class="mention hashtag" rel="nofollow noopener" target="_blank">#functional</a> programming. Deadline for application is 15th of February 2025.Please get in touch if interested, here's the official call: <a href="https://www.kent.ac.uk/scholarships/search/FN15COMPGR01" rel="nofollow noopener" translate="no" target="_blank">https://www.kent.ac.uk/scholarships/search/FN15COMPGR01</a>

Les capsules du prof Lutz<a href="https://jasette.facil.services/@zigong" class="u-url mention" rel="nofollow noopener" target="_blank">@zigong</a> Fun fact: André Joyal, un correspondant de Grothendieck (d'une première lettre du moins), est né à 10 minutes d'ici. <a href="https://webusers.imj-prg.fr/~georges.maltsiniotis/ps/lettreJoyal.pdf" rel="nofollow noopener" translate="no" target="_blank">https://webusers.imj-prg.fr/~georges.maltsiniotis/ps/lettreJoyal.pdf</a><a href="https://mamot.fr/tags/AlexandreGrothendieck" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlexandreGrothendieck</a> <a href="https://mamot.fr/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a>

MSP GroupHey You'se!Applications for PhD scholarships (UK students fully funded, international students part funded) in Computer & Information Sciences at Strathclyde are *open*.Details on applications within <a href="https://mastodon.acm.org/@mspstrath" class="u-url mention" rel="nofollow noopener" target="_blank">@mspstrath</a> are here:<a href="https://msp.cis.strath.ac.uk/phd2025-JARSS.html" rel="nofollow noopener" translate="no" target="_blank">https://msp.cis.strath.ac.uk/phd2025-JARSS.html</a>*Deadline* 25th November, 2024.Please share!<a href="https://mastodon.acm.org/tags/dependent_types" class="mention hashtag" rel="nofollow noopener" target="_blank">#dependent_types</a> <a href="https://mastodon.acm.org/tags/type_theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#type_theory</a> <a href="https://mastodon.acm.org/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#logic</a> <a href="https://mastodon.acm.org/tags/FormalMethods" class="mention hashtag" rel="nofollow noopener" target="_blank">#FormalMethods</a> <a href="https://mastodon.acm.org/tags/Coalgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#Coalgebra</a> <a href="https://mastodon.acm.org/tags/functional_programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#functional_programming</a> <a href="https://mastodon.acm.org/tags/homotopy_type_theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#homotopy_type_theory</a> <a href="https://mastodon.acm.org/tags/ProgrammingLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#ProgrammingLanguages</a> <a href="https://mastodon.acm.org/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mastodon.acm.org/tags/AppliedCategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#AppliedCategoryTheory</a> <a href="https://mastodon.acm.org/tags/HumanFactors" class="mention hashtag" rel="nofollow noopener" target="_blank">#HumanFactors</a>

Counting Is HardI wrote up the post on Weihrauch reducibility & Lenses. Would appreciate any comments / boosts etc.<a href="https://www.countingishard.org/blog/weihrauch-reducibility-as-a-lens" rel="nofollow noopener" translate="no" target="_blank">https://www.countingishard.org/blog/weihrauch-reducibility-as-a-lens</a><a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#computability</a> <a href="https://mathstodon.xyz/tags/complexity" class="mention hashtag" rel="nofollow noopener" target="_blank">#complexity</a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

amen zwa, esq.There are many <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> textbooks with <a href="https://mathstodon.xyz/tags/programmer" class="mention hashtag" rel="nofollow noopener" target="_blank">#programmer</a> or <a href="https://mathstodon.xyz/tags/programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#programming</a> in their titles. Invariably, they all start out with the precise definitions of categories, limits, colimits, functors, natural transformations, adjunctions, presheaves, .... Then, in the last page of the last section of the last chapter, they make vague references to programming language semantics, rather purfunctorily (CAUTION: that English word is not related to CT functor, profunctor, and the like).No, not <a href="https://mathstodon.xyz/tags/Bartosz" class="mention hashtag" rel="nofollow noopener" target="_blank">#Bartosz</a>'s guidebook, "Category Theory for Programmers". This one is, true to its title, for programmers.<a href="https://github.com/hmemcpy/milewski-ctfp-pdf" rel="nofollow noopener" translate="no" target="_blank">https://github.com/hmemcpy/milewski-ctfp-pdf</a>

Thomas<a href="https://mas.to/tags/RobertRosen" class="mention hashtag" rel="nofollow noopener" target="_blank">#RobertRosen</a> in Life Itself on physics. This statement has a sound mathematical foundation, much more so than the one people adhering to Reductionalism and Determinism can claim. There is a reason why his work is still not getting the attention it deserves. <a href="https://mas.to/tags/philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#philosophy</a> <a href="https://mas.to/tags/methodology" class="mention hashtag" rel="nofollow noopener" target="_blank">#methodology</a> <a href="https://mas.to/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mas.to/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mas.to/tags/biology" class="mention hashtag" rel="nofollow noopener" target="_blank">#biology</a>

ThomasWorking my way through Robert Rosen "Life Itself", for me a journey as instructive, demanding and profound as Hans Werner Arndt's "Methodo scientifica pertractatum". It takes time, research, re-reads. Friends are with me on the journey - there are no easy answers but a lot of wisdom. Rosen was an excellent teacher. <a href="https://mas.to/tags/RobertRosen" class="mention hashtag" rel="nofollow noopener" target="_blank">#RobertRosen</a> <a href="https://mas.to/tags/science" class="mention hashtag" rel="nofollow noopener" target="_blank">#science</a> <a href="https://mas.to/tags/metascience" class="mention hashtag" rel="nofollow noopener" target="_blank">#metascience</a> <a href="https://mas.to/tags/modeling" class="mention hashtag" rel="nofollow noopener" target="_blank">#modeling</a> <a href="https://mas.to/tags/measurement" class="mention hashtag" rel="nofollow noopener" target="_blank">#measurement</a> <a href="https://mas.to/tags/philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#philosophy</a> <a href="https://mas.to/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mas.to/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#logic</a> <a href="https://mas.to/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

Thomas<a href="https://mas.to/tags/RobertRosen" class="mention hashtag" rel="nofollow noopener" target="_blank">#RobertRosen</a> in Life Itself applies <a href="https://mas.to/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> to make sense of so many discussions in <a href="https://mas.to/tags/science" class="mention hashtag" rel="nofollow noopener" target="_blank">#science</a> and <a href="https://mas.to/tags/philosphy" class="mention hashtag" rel="nofollow noopener" target="_blank">#philosphy</a>, A deep read for those who no longer believe in magical formalism, highly recommended.

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