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
20.5.2025 07:13banger: Lawvere theories and finitary monads are both categories enriched in finitary endofunctors, and taking (power-preserving) functors...just completed a proof as a song's drop was coming 😙👌
17.5.2025 10:21just completed a proof as a song's drop was coming 😙👌she PhD on my thesis til I submit
13.5.2025 11:55she PhD on my thesis til I submitPSA: 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'.
13.5.2025 11:53PSA: 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...well I've seen crackpot papers but I've never seen crackpot phd theses before... yikes
13.5.2025 08:09well I've seen crackpot papers but I've never seen crackpot phd theses before... yikesthe original italian brainrot was the Italian school of geometers change my mind
12.5.2025 20:13the original italian brainrot was the Italian school of geometers change my mindlmao epub files are just zipped folders of html pages?
12.5.2025 15:49lmao epub files are just zipped folders of html pages?made this today send your energy for thesis writing pls
9.5.2025 16:10made this today send your energy for thesis writing plsvisiting TalTech, hit by this banger
7.5.2025 05:09visiting TalTech, hit by this bangerautoencoders is when you try to split an idempotent
7.5.2025 05:07autoencoders is when you try to split an idempotentfor 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
30.4.2025 17:27for the first time I used the qualitative-quantitative bridge afforded by quantitative predicate logic (https://arxiv.org/abs/2406.04936) to...🤚 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 *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?
30.4.2025 14:25are there known ways to talk about 'situated' mathematical structures, i.e. to talk about a structure (e.g. a set, a group) be...finally have a word for this concept, obsessed
30.4.2025 08:20finally have a word for this concept, obsessedubuntu is driving me insane, what do you mean the terminal application runs on python
29.4.2025 13:49ubuntu 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 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:
https://bigthink.com/starts-with-a-bang/cecilia-payne-discovered-what-stars-made-of/
20.4.2025 15:37the story of how we discovered what the stars are made of and who made the discovery:...state-sanctioned deportation in the US, state-sanctioned transphobia in the UK... what a sad time. sending thoughts to y'all affected by this 😞❤️🩹
18.4.2025 11:03state-sanctioned deportation in the US, state-sanctioned transphobia in the UK... what a sad time. sending thoughts to y'all affected by...what an absolute disgrace of event. fuck the breakthrough prize.
https://www.math.columbia.edu/~woit/wordpress/?p=14572
17.4.2025 06:15what an absolute disgrace of event. fuck the breakthrough prize.https://www.math.columbia.edu/~woit/wordpress/?p=14572somehow 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 💔)
8.4.2025 17:10somehow 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...⬆️
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