@BartoszMilewski@mathstodon.xyz

Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Jun 01, 2026

@sjoerd_visscher@types.pl
I worked out the right adjoints to profunctor composition. Do you already have it in your library?
https://v15.next.forgejo.org/BartoszMilewski/Categories/src/branch/main/src/ProfClosed.hs

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 29, 2026

In the future, body shaming will be the AI making fun of people who have bodies

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 25, 2026

Programmers might be able to compete with the AI after all. As long as human intellectual labor is cheaper.

https://www.aol.com/finance/microsoft-ceo-sends-shocking-message-163700210.html

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 23, 2026

Another installment in the series on Double Categories and Profunctor Equipments.
https://bartoszmilewski.com/2026/05/23/tabulation-tribulations/

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 19, 2026

A new post in the series on double categories and profunctor equipment.
https://bartoszmilewski.com/2026/05/18/bending-yanking-and-cartesian-squares-in-double-categories/

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 16, 2026

Another blog post in the series on profunctor equipment
https://bartoszmilewski.com/2026/05/16/profunctor-equipment-in-haskell/

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 15, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl Half of category theory is struggling with conventions. I decided to use the convention where the direction of the profunctor arrow agrees with the direction of morphisms in the hom-functor.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 15, 2026

@sjoerd_visscher@types.pl
I decided to write a post about my toy implementation of profunctor equipments. Here's the preview.
https://bartoszmilewski.com/?p=14290&preview=1&_ppp=770ff31cfc

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz This is also known as a Bool-enriched profunctor

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

TIL that Haskell module names cannot start with a number. I have a bunch of Haskell files for my book, whose names start with chapter numbers. I can compile them, but when I tried to add them to a cabal file, I was thwarted. What could be the reason for such a restriction, one wonders.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz Yes, trying to do dependent types in Haskell is a challenge. How would you encode the simplest category of elements of a functor. An object is a type a and a value x :: f a. A morphism from (a, x) to (b, y) is a function u: a->b such that fmap u x = y. If you can encode this, then tabulation should be relatively easy.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @BartoszMilewski@mathstodon.xyz

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz A morphism is built from two pairs of objects (a, b) and (a', b') and a pair of arrows (u: a -> a', v: b -> b'). They have to satisfy a commuting square that uses lmap and rmap.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @BartoszMilewski@mathstodon.xyz

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz It seems to me like you're defining a subcategory of Hask by imposing a Constraint on objects. So a Tabulator would be a class that takes two categories and a profunctor between them. It would have two projections giving objects in these two categories, and a projection that gives the element of the type given by the profunctor on these two objects. Does it make sense?

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz Well, I'm afraid my code is really a toy example based on endofunctors. What I really need is categories and functors between them. What definition of a category did you use?

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @BartoszMilewski@mathstodon.xyz

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz Next I want to test the definition of tabulation in Prof

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 13, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl @6d03@mathstodon.xyz Yes, I also used (Co-)Star as my Conjoint/Companion.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 12, 2026

Replying to @6d03@mathstodon.xyz

@6d03@mathstodon.xyz For me they're horizontal lines, although they connect two areas that are on top of each other, so I see your point. I've been following the conventions of David Jaz Myers. https://arxiv.org/abs/1612.02762

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 12, 2026

Replying to @6d03@mathstodon.xyz

@6d03@mathstodon.xyz No, they are horizontal, but I use string diagrams. For instance, this is vertical composition of 2-cells:

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 12, 2026

Haskell implementation of 2-cells in profunctor equipment

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 11, 2026

I just realized that Chekhov's Gun is an example of linear logic. It's a premise that has to be consumed at some point in the plot.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 08, 2026

Replying to @vnikolov@ieji.de

@vnikolov@ieji.de Joking aside, ultrafinitists actually had a conference. Not at any math department, but at a philosophy department, where they are tolerated. I even recognize some names. https://philosophy.columbia.edu/events/ultrafinitism-physics-mathematics-and-philosophy

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 07, 2026

Replying to @johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz Our worm-like ancestors were cyclops. When they decided to start swimming, the central eye squeezed out two side eyes and was itself reduced to the pineal gland that to this day regulates our circadian cycle. https://theconversation.com/our-modern-vision-evolved-from-an-ancient-one-eyed-worm-creature-278120

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 06, 2026

Replying to @Andrev@types.pl

@Andrev @bjacobs What's the alternative? European citizens are running Windows and IOS, using Google for searches and Chrome and Firefox for browsing, Chat GPT and Claude for AI. It reminds me of the Aesop's story of the wolf and the house dog. "What's that on your neck? asked the wolf..."

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 06, 2026

Replying to @bjacobs@social.edu.nl

@bjacobs Why is Europe so far behind the US and China? There must be some deep systemic issues that work against European innovation. Why isn't there a European Microsoft or Apple and, more recently, an AI company on a par with the Americans? It's definitely not for want of intellectual power in Europe.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 06, 2026

Replying to @h0gh@mastodon.social

@h0gh@mastodon.social @drmakimber@mathstodon.xyz I bet they blame it on Dedekind cuts

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 06, 2026

Ultrafinitists wanted to organize a conference but the only place that still had rooms available was the Hilbert Hotel

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 02, 2026

Replying to @julesh@mathstodon.xyz

@julesh@mathstodon.xyz The main problem is that the exponentials diverge, so the rich are getting richer, while the poor are getting relatively poorer. A quarter of American household have zero or negative net worth, so they are getting poorer with time.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 01, 2026

Replying to @dpiponi@mathstodon.xyz

@dpiponi@mathstodon.xyz With an obvious sequel: They movie you're pitching wins and Oscar, which is then used to highjack a metro train in Berlin.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · May 01, 2026

Replying to @dpiponi@mathstodon.xyz

@dpiponi@mathstodon.xyz The goal, though, is noble: Using Banach-Tarski, produce two Earths, one red, one blue.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 28, 2026

Filling my whiteboard with string diagrams. Comma objects and Kan extensions in a double category

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 28, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl My experience was that any optics I could put my hands on has a Tambara representation and that this is related to Tannakian reconstruction. So I'm looking for a grand unified theory of optics, and double categories look promising in this respect. At the very least they unify regular optics with enriched optics.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 27, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl Have you seen this paper? It shows that Tambara modules form a proarrow equipment. https://arxiv.org/abs/2210.13443

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 24, 2026

Replying to @sjoerd_visscher@types.pl

@sjoerd_visscher@types.pl This is some very impressive library. Are you planning on writing more detailed documentation for it? Translating from category theory to Haskell involves a lot of implementation decisions, so some kind of roadmap would be very useful.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 24, 2026

Replying to @varkor@mathstodon.xyz

@varkor@mathstodon.xyz Thanks, I'll correct this. It was the result of my perusing Grandis & Pare, where they say "the (strict) double category Dbl consisting of weak double categories, lax double functors (as horizontal arrows) and colax double functors (as vertical arrows), with suitable cells." So this works for pseudo or weak double categories.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 24, 2026

I decided to popularize double categories using profunctor equipment as a model.
https://bartoszmilewski.com/2026/04/24/profunctor-equipment/

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 23, 2026

Finishing a blog post on profunctor equipments.

Unit and counit of the adjunction between companions and conjoints in a double category.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 21, 2026

Homeopathy in computer science: Take a random sequence and sort it ten times. How much of the original sequence can you recover?

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 18, 2026

Replying to @julesh@mathstodon.xyz

@julesh I guess it satisfies the first definition. But notice that it's subjective. A "hallucination" doesn't meet our expectations. But whose fault is it?

an unattractive or unsatisfactory feature, especially in a piece of work or in a person's character.
responsibility for an accident or misfortune.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 17, 2026

Replying to @julesh@mathstodon.xyz

@julesh But how is this a fault? The LLM provides the most plausible sounding answer to your question. It's painting a picture or writing a novel for you. You might not like it because you have a particular esthetic in mind. A novel is not wrong because it cites a non-existing paper to move forward the plot.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 06, 2026

Replying to @regehr@mastodon.social

@regehr@mastodon.social There's also the option of installing an electrical outlet in the shower... Though, on second thought...☠️

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Apr 06, 2026

Replying to @regehr@mastodon.social

@regehr@mastodon.social Has anyone tried using an iPhone in the shower? They are supposed to be water resistant and there is a ToDo applet on them.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Mar 08, 2026

Replying to @GoodAaron@mastodon.social

@GoodAaron@mastodon.social And of course "Dune" -- the strugles against colonialism and theocracy

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Mar 06, 2026

Replying to @johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz That reminds me of the lemur aye-aye that also has very long fingers.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Feb 17, 2026

Democracy is like health: You don't appreciate it until you lose it.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Dec 20, 2025

Replying to @johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz The US has a huge infrastructure debt. All those overhead power lines that snap every time the wind starts blowing. Not to mention the esthetic nightmare of tangles of sky-obscuring wires in every residential area. Most Americans don't even notice it.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Dec 16, 2025

Replying to @johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz @alisonkiddle@mathstodon.xyz I whould divide the two numbers and see if the result is less than one. The advantage is that you can cancel the factor of 2⁴

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Aug 09, 2025

Replying to @johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz @gregeganSF@mathstodon.xyz In the modern world you need a PhD to realize how insignificant the chances of you advancing science really are.

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Aug 05, 2025

Replying to @colincornaby@mastodon.social

@colincornaby Ever since people realized that you can sear a steak on a GPU running LLM, the Nvidia stock is skyrocketing

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Bartosz Milewski @BartoszMilewski@mathstodon.xyz · Jul 01, 2024

Replying to @EUCommission@ec.social-network.europa.eu

@EUCommission@ec.social-network.europa.eu I'm using uBlock origin to block ads. But I'm paying a ransom to Facebook.

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