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  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...

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  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

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  algebra is the OG. shout-out to medieval Arab mathematicians.

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  RE: https://mastodon.social/@el_t9/116669755243857552 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 ⬆️)

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  gutted to learn floc workshops are run on weekends

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  hydra writing: when every paper divides into two papers, ad infinitum

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  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.

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  potluck conference catering to save on registration fees

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  RE: https://mathstodon.xyz/@j2kun/116647564681336614 71k points wtf

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  RE: https://mathstodon.xyz/@Log3overLog2/116648032591518662 is there a depths of Wikipedia account on Mastodon

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  RE: https://mathstodon.xyz/@highergeometer/116650966112669202 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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  RE: https://mathstodon.xyz/@mc/116613311649610117 yay turns out Shulman's notes do it with faithful clubs

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  RE: https://social.vivaldi.net/@RosaCtrl/116629962550751648 "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 r...

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  so satisfying when the lemmata lem

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  does anyone know why Fiore-Plotkin-Turi in 'Abstract Syntax and Variable Binding' (https://doi.org/10.1109/LICS.1999.782615) & subsequent works study algebraic structures on *sets* of types rather than *categories*?

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  RE: https://mathstodon.xyz/@mc/116613310898838315 ok actually you can get away with this

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  it's a quantifier only if it is indexed over an internal sort, otherwise it's just an infinitary connective

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  📣📰 **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!

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  btw the RSS feed in my website is back in case you want to follow there https://matteocapucci.eu/feed/atom.xml

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  it appears I am speedrunning Goguen's research: categorical systems theory, fuzzy logic, quite a bit of categorical logic...

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  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...

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  Little survey on the topic of formalization and publication (in CS) Do you think we are still at a point in which mere formalization (bearing no additional insights besides a reassurance of correctness) counts as an additional substantial contribution to a paper?

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  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

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  this ML paper we are writing is so frustrating because the sota we are comparing against is so bad no comparison is really fair without tweaking and adjusting and conceding so much that at the end of the day our technique is only 'significantly' better. it's like a CNC tool it's being evaluated on how well it can chip rocks to make them sharp.

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  RE: https://mathstodon.xyz/@mc/116475784226037488 'write this paper but never use these words. do not make mistakes.'

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  RE: https://wandering.shop/@adapalmer/116477506222415129 this is great, in fact we should ban any advertisment to children

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  sometimes I'm at odds with coming across as immodest and expressing how much I think some piece of math I discovered is cool. if I praise it it's because I think it doesn't belong to me, in fact, I was merely lucky to come across it.

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  Claude 4.7 is an *idiot savant*: it is very 'clever', as in it can take instructions involving task-specific knowledge (e.g. 'write an example of this construction') and succesfully complete it, but it is very 'dumb' as it's understanding is definitely still a pose. It misses the big picture and constantly overlooks stuff. But what I'm still amazed by is how fast its capabilities degrade with time. These models have O(1M) context wi...

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  am I late to the party https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy

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  ok firefox is falling part in slow motion, does anyone have recommendations for a good browser? adware and spyware are a no-no, effective mobile-desktop syncing is a must