Category Witch

Mathematics is fun

[Category Witch @JadeMasterMath]

@mattecapu Wondering how that's even symmetric? (is it?) I suppose by taking some left or right adjoints you can turn L \tens M into M \tens L?

[Category Witch @JadeMasterMath]

@mattecapu :eyes:

[Category Witch @JadeMasterMath]

@TonyTheLion2500 They don't tell you this but presheaves are better than sheaves even though they have the derogatory name

[Category Witch @JadeMasterMath]

@davidad I've been saying! (e.g. my thesis)

[Category Witch @JadeMasterMath]

@no_earthquake Live from New York it's Saturday Night!

[Category Witch @JadeMasterMath]

@Glorbutron @davidad Oh fair enough. Is that true in some pathological Hilbert spaces?

[wordgrammer @wordgrammer]

I can suggest an equation that has the potential to impact the future:

𝐍𝐚𝐭(𝐇𝐨𝐦(−, 𝐶), 𝐹) ≅ 𝐹(𝐶) + AI

Given a category 𝒞, a functor 𝐹 : 𝒞ᵒᵖ → 𝐒𝐞𝐭, and an object 𝐶 ∈ 𝒞.

This equation combines Yoneda’s famous Yoneda lemma, which relates a category (𝒞) to a functor (𝐹: 𝒞ᵒᵖ → 𝐒𝐞𝐭) and the speed of light (𝐶 ∈ 𝒞), with the addition of Al (Artificial Intelligence). By including Al in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for Al to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as healthcare, transportation, and technology.

[Category Witch @JadeMasterMath]

@garvidge I don't know if computers just take binary input, at least that's a pretty reductionist way of looking at it. How would this capture running two programs at once for example.

By the way, the set in question is infinite sequences not finite ones.

[Category Witch @JadeMasterMath]

I think this is more like a particular choice of semantics for programs, which makes sense in some contexts but not others. Or maybe I'm missing the point that all programs can be reduced to these somehow?

[danb @dnbt777]

ok
https://t.co/SQHvZhhDZC

[Category Witch @JadeMasterMath]

Bohmian interpretation of quantum mechanics

[Physics In History @PhysInHistory]

Mention one scientific opinion that you’d defend like this ✍️

[Category Witch @JadeMasterMath]

What is pip then?

[Dmitrii Kovanikov @ChShersh]

Sometimes I don't know how else to convince people to try Functional Programming

[Category Witch @JadeMasterMath]

@BarbaraFantechi You MUST include the points at infinity

[Category Witch @JadeMasterMath]

Projective geometry is when you draw a lot of lines

[Jay Cummings @LongFormMath]

Projective geometry 😍

[Category Witch @JadeMasterMath]

@fabgenovese If the product is free then you are the product!

[Category Witch @JadeMasterMath]

@myers_jaz @BowToChris The reason for this is because a lax functor 1 -> D is the same as a monad in D, so making it normal means there's no algebras and you have to add them back in to get an equivalence

[Category Witch @JadeMasterMath]

Still getting weirded out about how:

Lax functors C -> Span

And

Lax normal functors C -> Prof

are the same thing

[Category Witch @JadeMasterMath]

@myers_jaz @BowToChris Well you've got an equivalence
normal lax C -> Alg(D)

And

lax C -> D
So Alg is actually the right adjoint. I think that makes normal lax functors a coreflective subcategory?

[Category Witch @JadeMasterMath]

@BarbaraFantechi @themathgay 👀 what is it an Euler characteristic of?

[Category Witch @JadeMasterMath]

People just learning that Israel is an authoritarian theocracy are like:

[Noah Smith 🐇🇺🇸🇺🇦🇹🇼 @Noahpinion]

Whoa I just learned that interfaith marriage is illegal in Israel!!

What the fuck?? This is insane.

[Category Witch @JadeMasterMath]

@BowToChris Well there's the thing where you invert spans to get profunctors but that only gets discrete categories so not quite