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banger: Lawvere theories and finitary monads are both categories enriched in finitary endofunctors, and taking (power-preserving) functors...

banger: Lawvere theories and finitary monads are both categories enriched in finitary endofunctors, and taking (power-preserving) functors into another (powered) category is taking models
so why are models of a Lawvere theory and algebras of the corresponding monad the same? because the former, as an enriched category, is the Cauchy completion of the latter, and thus the power-preserving functors out of it are the same!

https://www.sciencedirect.com/science/article/abs/pii/S002240491400036X

just completed a proof as a song's drop was coming 😙👌

just completed a proof as a song's drop was coming 😙👌

she PhD on my thesis til I submit

she PhD on my thesis til I submit

PSA: yoneda is when a morphism out of a free object is determined by its action on generators. so every time you represent a linear map as a...

PSA: yoneda is when a morphism out of a free object is determined by its action on generators. so every time you represent a linear map as a matrix, you can introduce it saying 'by Yoneda'.

well I've seen crackpot papers but I've never seen crackpot phd theses before... yikes

well I've seen crackpot papers but I've never seen crackpot phd theses before... yikes

the original italian brainrot was the Italian school of geometers change my mind

the original italian brainrot was the Italian school of geometers change my mind

lmao epub files are just zipped folders of html pages?

lmao epub files are just zipped folders of html pages?

made this today send your energy for thesis writing pls

made this today send your energy for thesis writing pls

visiting TalTech, hit by this banger

visiting TalTech, hit by this banger

autoencoders is when you try to split an idempotent

autoencoders is when you try to split an idempotent

for the first time I used the qualitative-quantitative bridge afforded by quantitative predicate logic (https://arxiv.org/abs/2406.04936) to...

for the first time I used the qualitative-quantitative bridge afforded by quantitative predicate logic (https://arxiv.org/abs/2406.04936) to backport a quantitative thing (bayesian update) to qualitative land and thus debug a qualitative definition

🤚 abuse of notation👉 *notational solecism*

🤚 abuse of notation
👉 *notational solecism*

are there known ways to talk about 'situated' mathematical structures, i.e. to talk about a structure (e.g. a set, a group) be...

are there known ways to talk about 'situated' mathematical structures, i.e. to talk about a structure (e.g. a set, a group) be *somewhere* in a space?

my first instinct is to use sheaves of Xs. X(U) answers the question 'what part of X is in U?' then you can situate a specific X at some point p by producing the skyscraper sheaf at p valued at X. but I've never seen this intepretation of sheaves! have you? does it make sense? do presheaves suffice?

finally have a word for this concept, obsessed

finally have a word for this concept, obsessed

ubuntu is driving me insane, what do you mean the terminal application runs on python

ubuntu is driving me insane, what do you mean the terminal application runs on python

> after lots of unsuccessful googling, I ask chatgpt how to swap fn and ctrl in Ubuntu> it says it can't be done but maybe...

> after lots of unsuccessful googling, I ask chatgpt how to swap fn and ctrl in Ubuntu
> it says it can't be done but maybe there's a 'swap fn and ctrl keys' in the bios options
> I roll my eyes
> check
> there is indeed a bios level option to do exactly that lmao

the story of how we discovered what the stars are made of and who made the discovery:...

the story of how we discovered what the stars are made of and who made the discovery:

https://bigthink.com/starts-with-a-bang/cecilia-payne-discovered-what-stars-made-of/

state-sanctioned deportation in the US, state-sanctioned transphobia in the UK... what a sad time. sending thoughts to y'all affected by...

state-sanctioned deportation in the US, state-sanctioned transphobia in the UK... what a sad time. sending thoughts to y'all affected by this 😞❤️‍🩹

what an absolute disgrace of event. fuck the breakthrough prize.https://www.math.columbia.edu/~woit/wordpress/?p=14572

what an absolute disgrace of event. fuck the breakthrough prize.

https://www.math.columbia.edu/~woit/wordpress/?p=14572

somehow managed to be in Glasgow for 4 days without seeing a single cloud and abundantly enjoyed of the sun. nice try, but I'm staying...

somehow managed to be in Glasgow for 4 days without seeing a single cloud and abundantly enjoyed of the sun. nice try, but I'm staying in Italy (I miss you too though 💔)