deaths-accountant

[deaths-accountant]

F(X,M) is the direct sum of X copies of M. In the category of Abelian groups the direct sum is the coproduct, and I assume this is so for commutative monoids.

The universal property of the coproduct says that for any commutative monoid A, and homomorphisms f_x: M_x -> A, there must be a unique homomorphism f: F(X,M) -> A such that f of the inclusion of M_x into F(X,M) is the same as f_x.

Taking f_x to be id_M for each M_x, there must be a unique homomorphism Σ: F(X,M) -> M such that Σ(inclusion_x(m))=m for all x and m.

But the images of the inclusions are precisely the singleton functions you mention, so this is exactly what you asked, and proving that sums work boils down to proving the universal property of the coproduct is universal, and that F(M,X) is the coproduct. I think these are both easy to do without circularity.

A "product" is something you do to a sequence with finite support taking values in a monoid M. A sum is something you do to an arbitrary function with finite support taking values in a commutative monoid M, which you could think of as a "finite M-multiset". I've said this before.

#maths

[deaths-accountant]

it would be kind of cool and kind of funny if third world labour being cheaper for labelling meant machine learning models started to disproportionately reflect third world perspectives.

[deaths-accountant]

If you like the other end, best way to support us is through patreon. And we’ve got a bunch of cool extra content there, like 80+ exclusive comics

[deaths-accountant]

[deaths-accountant]

IM FUCKING SCREAMING

[deaths-accountant]

Photos from my friend who is a vet tech

[deaths-accountant]

[Friend glancing at a file I left open on my laptop] Aww, they keep a list of all the compliments people give them, that's cute. [Notices a second file titled Compliments From People I Actually Respect] Hm

[deaths-accountant]

Caroline Polacheck | Dang Live on The Late Show

#that is hilarious and also my worst nightmare #<-lying I have many worse nightmares

[deaths-accountant]

for the last time she can't reclaim that

ok but we're all missing the important question here... WHO in the vatican has taught the spanish-speaking pope how to say faggotry in italian. how on earth did it come up. was it a prank. was it political sabotage. is there homosexual tomfoolery afoot in santa marta. I need to know more

[deaths-accountant]

we need to give him a bigger allotment fast I fear

Reverse unpopular opinion: the Unabomber

The lowhanging fruit here is "transitioning would've saved [ALLOTMENT EXCEEDED]"

More seriously: sort of analogously to my answer re:anprims, useful indicator light for whether or not someone is a raging dipshit who I shouldn't bother engaging with

And I guess most sincerely: Ted Kaczynski seems like a genuinely brilliant and troubled person who became lost and isolated, and I feel for him, even if that is typically overshadowed by other things when I think about him

[deaths-accountant]

ok but we're all missing the important question here... WHO in the vatican has taught the spanish-speaking pope how to say faggotry in italian. how on earth did it come up. was it a prank. was it political sabotage. is there homosexual tomfoolery afoot in santa marta. I need to know more

[deaths-accountant]

the main driving force in my life is acquiring information. if you ever see me doing something stupid please understand its because i have probably developed some bizarre idea about how to acquire more information and i have disregarded other concerns ("safety," "politeness") in favor of my ultimate goal. what am i going to do with this information? nothing at all. i am going to sit on it like a dragon sits on its golden hoard. dragons dont need gold to buy anything they are just using it as some type of really big couch or sensory sand type of situation. this is my relationship to information. in the past i have been happy to eat villagers in order to acquire my information but i am trying to be better now and only blackmail them, which i understand is more polite in many human cultures. im losing track of this metaphor. someone tell me a secret.

#sounds like a mistake

[deaths-accountant]

why's youtube recommending me this gay shit

oh. carry on then

[deaths-accountant]

back on earth they've identified a really weird transitionary link between the modern catgirl and early hominids and they're calling it "mankind"

[deaths-accountant]

got blood work done today and i just remembered a time i got blood work done as a teen. after the nurse drew like 6 vials of the stuff, i asked him “is all that mine?” and he said “not any more” and walked off

[deaths-accountant]

it's ok he can reclaim it

tha pope said Faggot

#because of the silly hat

[deaths-accountant]

Got drunk and misgendered myself last night can we cancel me