Timeline for What is the correct statement of Theorem 4.2 in Street's "Parity Complexes"?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2022 at 14:48 | comment | added | Simon Forest | @TimCampion: Sorry about that … My article was already too long, so that I had to put a stop to details and remarks. | |
| Jan 3, 2022 at 14:37 | vote | accept | Tim Campion | ||
| Jan 3, 2022 at 14:37 | comment | added | Tim Campion | @SimonForest I definitely agree it seems appropriate to modify the definition of parity complex in order to get 4.2 to go through; I was just confused that you did this without commenting about how the definition you use compares to what Street says in either of the two versions of his work. The bottom line is that Street's work, though groundbreaking, left us with a bit of a mess. Fortunately, it seems that you have cleaned up the mess completely! I think it just pays to be clear about what the cleanup job entailed, and not to downplay it out of excessive modesty. | |
| Jan 3, 2022 at 14:26 | comment | added | Simon Forest | (Timer for editing, sorry) No, assuming the tightness of $\mu(x)$ is sufficient. As I said in my reply below, Theorem 4.2 does not hold fully with or without the corrigenda. Concerning the fact I made tightness part of the definition of Street, it seemed acceptable, since for me a parity complex should be defined so that the original statement of Theorem 4.2 holds for this definition. Also, Street's approach concerning his axioms seems to be "whatever works", so that morally tightness can be made part of the definition without too much concern. | |
| Jan 3, 2022 at 14:16 | comment | added | Simon Forest | @TimCampion: $\mu(x)$ is the graded set made of the $\mu(x)_p$. | |
| Jan 3, 2022 at 14:06 | answer | added | Simon Forest | timeline score: 5 | |
| Dec 29, 2021 at 2:01 | comment | added | Tim Campion | It appears that in Forest's definition on p. 12 (unfortunately, Forest, like Street, does not number all his definitions!) he adds a condition to the definition of a parity complex (the condition needed for Street's corrected claimed Thm 4.2 -- even though Street never made this condition part of a "corrected definition" of a parity complex), so that on p. 13 his counterexample is presumably something satisfying this condition... so I think I agree he's refuting the corrected version. But he doesn't explicitly say which version he's refuting! | |
| Dec 29, 2021 at 1:54 | comment | added | Simon Henry | I assume the corrected version is still false. But I'm not very familiar with this... You should ask Simon Forest or read his paper. | |
| Dec 29, 2021 at 1:48 | comment | added | Tim Campion | @SimonHenry Thanks. I am confused (and my confusion was not alleviated by reading Forest's paper without delving into the proofs) -- Street already provided a corrigendum correcting the statement of Theorem 4.2. Is Forest saying that the original statement of Theorem 4.2 is false (which was already "known", or at least expected), or is he saying that the corrected version of Thm 4.2 is false? | |
| Dec 29, 2021 at 1:30 | comment | added | Simon Henry | The person you want to talk to here I think is Simon Forest. I don't know if he is on MO, but you can have a look at his paper : arxiv.org/pdf/1903.00282.pdf where among other thing he shows that the theore; you are talking about is actually false without some additional assumptions. | |
| Dec 28, 2021 at 23:08 | history | edited | Tim Campion | CC BY-SA 4.0 |
deleted 1 character in body
|
| Dec 28, 2021 at 22:59 | history | edited | Tim Campion | CC BY-SA 4.0 |
edited title
|
| Dec 28, 2021 at 18:13 | comment | added | Tim Campion | I've just noticed two things I don't understand. First, what is $\mu(x)$? Is it the union $\mu(x) = \cup_{n=0}^p \mu(x)_n$? (and similarly for $\pi(x)$?) Second, Street says in the corrigendum that in Section 4 we must assume $\mu(x)$ is tight for every $p$ and every $x \in C_p$ -- but should we also assume that $\pi(x)$ is tight? | |
| Dec 28, 2021 at 17:51 | comment | added | Ivan Di Liberti | Experts will come. Meanwhile, maybe related papers: Henry, "Non-unital polygraphs form a presheaf category". Hadzihasanovic, "A combinatorial-topological shape category for polygraphs". Gagna et al, "Nerves and cones of free loop-free ω-categories". | |
| Dec 28, 2021 at 16:33 | history | asked | Tim Campion | CC BY-SA 4.0 |