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@JacquesC2@types.pl you must be reading a category theory paper 😆 /s
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Matteo Capucci
@mc@mathstodon.xyz
mastodon 4.7.2Mathematician (category theory for general systems theory & cybernetics), socialist, aspiring psycohistorian, meme enjoyer (shitpost is not endorsement).
Currently: ARIA double grantee, 🇮🇹 based, finishing my PhD @mspstrath
Custodian of CT Zulip, email me for an invite.
1857 Followers
223 Following
50 Posts
Joined April 26, 2022
Pronouns:
he/him
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if you are an European citizen, consider signing this EU petition to ask for the suspension of trade and academic agreements with Israel until they withdraw from Gaza and the West Bank. We pump billions of euros into a system that allows if not promotes tremendous atrocities and blatant violations of international law, this must stop.
Link below ⬇️ (or above ⬆️)
RE: @RosaCtrl@social.vivaldi.net
"From a business perspective, I actually think this announcement isn’t necessarily good news for OpenAI. There are few markets smaller and less lucrative than professional academic mathematics."
Idk why people think AI companies are trying to automate academics (maybe because they believe the companies' press releases?). The most lucrative market for phd-level math is finance. They're trying to sell robot grad students to trading companies.
algebra is the OG. shout-out to medieval Arab mathematicians.
are people reinventing synthetic mathematics from first principles?
https://arxiv.org/abs/2605.03868
Mumford and Friedman propose a 'practical' foundation of set theory with countable dependent choice, restricted power sets, and the existence of reals as an axiom. feels very arithmetic universe coded...
a goated writing technique is to first give a talk about the paper and then write the paper following the outline of the talk. it forces you to sketch the whole thing into some detail first, but without getting in the weeds of *actual* writing.
📣📰 **Double Preprint Alert! **📣📰
Quantitative Linear Logic
*Matteo Capucci, Robert Atkey, Charles Grellois, Ekaterina Komendantskaya*
https://arxiv.org/abs/2605.13348
Quantitative Linear Logic for Neuro-Symbolic Learning and Verification
*Thomas Flinkow, Ekaterina Komendantskaya, Matteo Capucci, Rosemary Monahan*
https://arxiv.org/abs/2605.13845
I present them quickly here https://matteocapucci.eu/two-preprints-in-quantitative-logic
Comments welcome!
RE: @Log3overLog2@mathstodon.xyz
is there a depths of Wikipedia account on Mastodon
so satisfying when the lemmata lem
hydra writing: when every paper divides into two papers, ad infinitum
it appears I am speedrunning Goguen's research: categorical systems theory, fuzzy logic, quite a bit of categorical logic...
71k points wtf
Every week I have a meeting which turned into 'cute computations in presheaf topoi' and it's just the most satisfying time. Today we figured out what the adjoints to the 'Cayley graph' functor going from N-sets to Graphs are.
The right adjoint is very easy (its infinite paths in the graph with the shift action), the left action is quite confusing but very satisfying to prove. It's fun to see the math solve its own problems!
A trick we end up using a lot is: represent functors as change of base along a map of sites, write the coend formula as a left adjoint, then compute the coend as the quotient of a big coproduct. This way you can easily define maps out of this object, by defining them on the coproduct and check that they respect the newly added equations.
The real art is to find a way to present the resulting quotient. In this case, can you figure out what it is?
Echoing here an interesting issue raised by Emily Riehl on how to make commutative diagrams accessible with LaTeX
https://categorytheory.zulipchat.com/#narrow/channel/241990-community.3A-discussion/topic/alt.20text.20for.20commutative.20diagrams/with/593535459
it's a quantifier only if it is indexed over an internal sort, otherwise it's just an infinitary connective
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@julesh@mathstodon.xyz yeah that's the non-business part of it (that and the 'publicity stunt', a bit like Boston Dynamics making its robots somersault)
does anyone happen to know what a comonad in spans amounts to or a cool example of one? it looks a bit like a cocategorical gadget.
tagging my trusted cocategories expert @JadeMasterMath@mathstodon.xyz
potluck conference catering to save on registration fees
btw the RSS feed in my website is back in case you want to follow there https://matteocapucci.eu/feed/atom.xml
ok actually you can get away with this
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@ohad@mathstodon.xyz @mevenlennonbertrand@lipn.info I really like this metaphor 😆 don't show me your underwear! but I expect it to be clean
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@JacquesC2@types.pl @maxsnew@types.pl I didn't quite read any Agda but I scavenged a LaTeX note under Notes/ that makes the point that even if there are equivalent definitions for universal objects in category theory, you prefer the representability ones @maxsnew@types.pl
Is this takeaway coming from the formalization effort? Also, is it a matter of making a canonical choice for all instances or are there actual benefits when using representability vs universal arrows or 'first-order' universal properties?
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@SvenGeier@mathstodon.xyz @julesh@mathstodon.xyz i'm skeptical of a great replacement, but we'll see!
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@jaklt@mastodon.social lol yeah I was familiar with the construction but not the minion name haha
though I'm now back to thinking your initial data should be a category
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@sjoerd_visscher@types.pl uh, thanks for spotting that. I forgot arxiv doesn't support that package and I need to find an alternative..
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like, would you ever pass a paper with a contribution that you wouldn't pass otherwise?
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@JacquesC2@types.pl @maxsnew@types.pl btw, when you approach a library like this, where do you start?
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this does not count as bragging because, really, sota is so bad
RE: @highergeometer@mathstodon.xyz
bus passenger looking at the mountain: LLMs will hallucinate science to death
bus passenger looking at the view: LLMs are helping scientists find work traditional archival tools didn't know the existence of
(yeah prolly not)
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I should have picked those notes up much earlier, they are exactly the flavour of logic I do (maybe through subliminal conditioning all this time?)
gutted to learn floc workshops are run on weekends
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@Paul_Taylor@mathstodon.xyz Thanks Paul, I also prefer to circumscribe the adjunction to weakening, or other issues get mixed up.
Exactly what kind of completeness are you working on?
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to be precise, their 'substitution algebras' are for F-sets, where F is finite sets = free cocartesian category on a single generator.
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@maxsnew@types.pl @JacquesC2@types.pl thanks! so much wisdom.
re your last question, they are but packaged in a different form I'd say
rather than giving a natural isomorphism, you show that certain arrows factor uniquely. it's really easy to go back and forth but nonetheless...
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@cbaberle@mathstodon.xyz @olynch@mathstodon.xyz I think here they implicitly work indexed, which shouldn't have strictness issues
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@JacquesC2@types.pl @MartinEscardo@mathstodon.xyz @egbertrijke@mathstodon.xyz @gallais@mamot.fr is this elaborated somewhere? how do you best organize it for formalization?
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@joannako@mathstodon.xyz lmao that's a good observation. 'what if we thought about things' is a surprisingly unpopular sentiment.