An abelian category is a category with zero object, products, coproducts, kernels, cokernels where mono are kernel and epi are cokernel (this definition is autodual); one of the axioms for regular (exact) categories is that the pullback of a regular epi is a regular epi, and since in abelian categories regular epi is equivalent to epi, one could ask to prove that

> the pullback of an epi is an epi

which is easy to axiomatize.

The proof that I know uses the fact that abelian categories are additive (not trivial to show). If for some reason an ATP would be able to prove the theorem (seriously?), I don’t think it would be intelligible at all.

Another thing I don’t expect an ATP to prove is that if E is an (elementary) topos then the slice category E/x is a topos (cartesian closedness is notoriously hard). Essentially, everything that requires you to go up the hill.

But I like to watch ATPs diverge :3c

That said, I’m becoming a fan of Z3 and rewriting techniques. Thank you for sharing this article ðŸ™‚

]]>I wish all is well with you.

I have two naive questions, when you project to the lowest Landau level (LLL), in p.2,

1) https://arxiv.org/abs/1603.03754 in eq.2, should you consider the \xi coordinate labeled

by general different electron indices ” j ” instead of the same ” i “?

say,

\langle\{z_i\} | \{\xi_ j ‘}\}\rangle ?

I meant in the usual Fourier transformation, the other basis coordinate should be a free (and summed over independent from “i “)?

Am I correct or wrong? (Should I regard this as a minor typo/mistake?)

2) Is this project to LLL, an exact result or only an approximation?

Thank you very much.

Best Wishes,

Juven

Whoopsy! Thank you for pointing that out

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