Comments for Annoying Precision

Comment on Groupoid cardinality by Mohamed Salaheldeen

Mohamed Salaheldeen — Tue, 22 Apr 2025 11:04:03 +0000

Sorry I don't understand how is EG equivalent to a point groupoid? I only see the collapse functor which as far as I understand is not an equivalence.

Comment on Coalgebras of distributions by Qiaochu Yuan

Qiaochu Yuan — Sat, 22 Mar 2025 12:16:03 +0000

In reply to matthewcushman.

Ah, I guess that’s a little confusing. It means the extension of scalars of to a coalgebra over , so the comultiplication is just being extended -linearly.

Comment on What’s a fire, and why does it – what’s the word – burn? by Shawn Hu

Shawn Hu — Tue, 11 Mar 2025 08:37:32 +0000

The title of this post reminded me of this [famous interview with Feynman](https://www.youtube.com/watch?v=N1pIYI5JQLE). In the first 2 minutes or so he gets around to describing, in great detail, what you said in the first three sentences of this post.

Comment on Coalgebras of distributions by matthewcushman

matthewcushman — Sun, 02 Mar 2025 03:44:50 +0000

Amazing, thanks! I'm a little confused by the last theorem though. What is meant by D[e]/e^2? (No epsilon key) If D is only a coalgebra I'm not sure how to interpret eg e^2.

Comment on Extracting the diagonal by columbus8myhw

columbus8myhw — Thu, 16 May 2024 21:28:16 +0000

I don't know how to format LaTeX on WordPress, but hopefully this image works.

Comment on Extracting the diagonal by columbus8myhw

columbus8myhw — Thu, 16 May 2024 21:20:30 +0000

Very interesting! I used your strategy to show that if $a_n$ is determined by the $n$th coefficient of $(ax^2+bx+c)^n$, then the generating series of $a_n$ is
$$frac1{sqrt{(b^2-4ac)x^2-2b+1}}.$$
I don't know if this result is already known. (I assume it is.)

Incidentally, in all your examples, as $rto0$, all the poles tend to either $0$ or $infty$. Is that true in general? If so, when you say to sum over poles in the unit circle, you could have instead said to sum over poles that don't blow up.

In short, that means the technique is that $D_F(r^2)$ is the sum of the residues of $frac1zF(rz,rz^{-1})$ over all poles that don't blow up as $rto0$.

Comment on Regular and effective monomorphisms and epimorphisms by E.

E. — Fri, 19 Apr 2024 19:44:55 +0000

Very interesting. As analyst, I am mostly familiar with Banach spaces. Can we have an explicit description of regular monomorphism and regular epimorphism. Are regular epimorphism surjective ?

Comment on Ideals and the category of commutative rings by Pete

Pete — Mon, 26 Feb 2024 21:16:45 +0000

You probably mean: "And in

the coslice category

for

a field is precisely the category of commutative

-algebras."

Comment on Fixed points of random permutations by Anonymous

Anonymous — Fri, 23 Feb 2024 15:49:49 +0000

Would you have published references to your "reasonably well-known exercises in combinatorics" and to your E(X^k)=B_k?

Comment on Introduction to string diagrams by Felix Pahl

Felix Pahl — Mon, 08 Jan 2024 12:40:18 +0000

Thanks for the nice post 🙂

I think in the equation after “is equal to” the last composition should be a tensor product?