Calling all scientists

[pozorvlak]

Can you please cast your eyes over this (173KB pdf) and give me a sanity check? To whatever level you can: if you understand the material and can critique it on that level, great, but if all you can do is check that I haven't absent-mindedly written "I am a fish" 500 times or left a "fill this bit in later" somewhere then that's wonderful.

If you're not sure whether this applies to you, it does.

Thanks!

Comments

[necaris.livejournal.com]

No "fill in later" bits found, I'm happy to report, and the few words I understood (e.g. "the", "let" and "an") seemed to make sense in context :-)

[randomchris.livejournal.com]

Your diagram at the bottom of page 3 appears to have some overlapping symbols (between the two curved arrows in the bottom right-hand corner). The same symbols in the first diagram on page 4 are also overlapping slightly.

[susannahf.livejournal.com]

Agreed. There's also overlapping in the top left-hand corner of the diag in Def 2.8 (bottom p3). Is the last diag on p8 meant to be lined up like that?

Yes, I just looked at the diagrams. I tried to read it, but my eyes did that slipping off the page thing after about a paragraph... Which is not to say that it's hard to read, just that I really really don't understand maths at that level ;)

On the upside though, there were no matches found when I searched for "fish"

[pozorvlak.livejournal.com]

I'm not happy with the last diagram on p8, but I don't know how to fix it. The idea is that every arrow (think "function") of a certain form has a "transpose", and we write "f is the transpose of g" as

f: A → UB
--------------
g: FA → B

or vice-versa. The transpose of the transpose of an arrow is the arrow itself. So I'm starting with an arrow, taking its transpose, showing that that's equal to something else and taking the transpose of this new thing, leaving me with something equal to the arrow I started with. The notation's standard in the field. Ideally, I'd like the lines to be a bit shorter.

[johnckirk.livejournal.com]

Yeah, I had the same trouble of this being beyond my level, despite phrases like "in the obvious way" or "it is easy to extend". I also had the same reaction to the last diagram on page 8, i.e. it looks as if it's misaligned, even if it's supposed to be like that; this may not be a problem for people who understand the maths involved.

[pozorvlak.livejournal.com]

Grargh. Most of those had actual proofs in, which my supervisor suggested I take out! Journals "prefer a condensed style", apparently :-) The proofs will be going in the thesis.

[pozorvlak.livejournal.com]

Great, thanks. That'll require a bit of grovelling in the manual to fix, but shouldn't be too hard.

[michiexile]

Downloaded. Printed. Will read tonight. Feedback tomorrow.

[pozorvlak.livejournal.com]

Great, thanks. Tomorrow's the submission deadline, so not too late tomorrow, please :-)

[adqam.livejournal.com]

Aha! Something to do in the office tomorrow that looks like work and isn't! Feedback then.

[pozorvlak.livejournal.com]

Thanks! But note that tomorrow's the submission deadline, so I won't be able to use feedback that comes too late. But it's all going in the thesis anyway, so everything's useful.

[nonstick.livejournal.com]

I take it references are alphabetical by order, rather than the order they appear in the text? I got a bit confused by the first one being [2].
Then my eyes glazed over..

[pozorvlak.livejournal.com]

Yeah. That's a matter of journal style, I think - not sure what these guys want, but my supervisor reckons it's not worth spending effort on until the paper's been accepted.

[michiexile]

Good call by your supervisor. Taste and consistency in these matters vary so Damn wildly.

Feedback

[michiexile]

So ... here are the things I reacted in any way on:

Definition 2.7: How is the notation introduced used? It only vaguely becomes clear in the last two pages of the paper, and not very clear even then.

Diagrams (1): Overlapping symbols.

Diagrams (3): Overlapping symbols.

Lemma 2.10: Is fork a well-known term in your corner of mathematics? I knew all the words except for this one in the paper.

Proof of 3.7, the weird fractions on p8: You might want to use \frac to get shorter lines?
Also you have a duplicate arrow on the left down side.

Same proof, last few lines: the fork gives that paragraph REALLY odd linespacing. Also the linebroken iso looks ugly.

Section 4, middle p10: ugly linebroken and overflowing equation.

Other than that - neat, cute and nice.

Re: Feedback

[pozorvlak.livejournal.com]

Def 2.7: I take your point. The idea is that if p ∈ P_n, then \hat p is a function A^n → A. That could be usefully clarified.

Fork: Well, my supervisor uses it all the time, and I think I've heard other people use it too. It means a diagram of that shape, such that γα = γβ, but &gamma is not necessarily a coequalizer and α is not necessarily equal to β.

3.7: They're not fractions, they're transposes. I think that notation is common among categorists, but I'll check. I'll try using \frac, but it might be tricky to get the vertical alignment right. Duplicate arrow: fixed now, thanks. I've displayed the fork, which fixed the linebroken iso.

Section 4: oh, yeah. Ugh! I changed "Is" to "We wish to show that", which makes things a lot better.

Thanks very much!

[metamoof.livejournal.com]

Extremely silly sanity checks, but you never know with these things:

Page 1 and onwards: you do mean operad and not operand, right? ;)

"It has been conjectured (though as far as I know, not proven) that the linear theories are those which can be presented by means of equations whose variables appear exactly once on each side, though possibly not in the same order." - That the looks either superfluous or incorrect given you generalisation in the previous sentence.

Definition 2.1, the Associativity condition "wherever this makes sense" seems a bit vague, given it has to be satisfied. Do you need to either rephrase or expand on that?

You may not be a fish, but an unexplained Cat appears at the bottom of Definition 2.7. Given that you do say earlier "We take the set of natural numbers N to include 0," a three-word definition of Cat might be in order.

There appears to be a random tickybox at the end of Lemma 2.10

Bottom of page 5: you're missing a fact. Ulness the lemma is the fact, in which case that sentence belongs on the top of page 6.

Given you have a tickybox at lemma 2.17 that these are actually intended.

Def 3.1: I take it epi is a technical term and not a sort of fit, or a weird mathematical symbol that is missing a \.

Ex. 3.5: is "w.r.t." acceptable? Should it not be written out?

Bottom of page 7: should the definition of the theorem not be on the following page, given the proof is there?

The equation at the bottom of page 8 looks squiffy to me. But then again, I'm an engineer, and don't do this pure maths lark.

Section 4 para 1 sentence 1: you've got a random ".," before "and is empty in all other arities." seing as the . appears to be significant, should there be a space before the ,?

Section 5: I always though myself to be a member of the cognoscenti, but I didn't know that.

And that's it from me.

Ouch. my head hurts. Can I go back to editing your Chron articles instead?

[metamoof.livejournal.com]

It is worth noting that, despite my hopes to the contrary, your paper has utterly failed to send me to sleep. This is probably a good thing.

[pozorvlak.livejournal.com]

"Operad" - yep, that's what I meant. I wrote about them here (http://pozorvlak.livejournal.com/67276.html#cutid1), but they're essentially a way of collecting together some operations which take varying numbers of arguments (so some take 2, some take 3, etc) and which satisfy some equations.

Tickyboxes - they just mean "End of proof", rather like "QED". They're reasonably standard these days.

Superfluous "the": I see what you mean. Not sure which is better.

Cat: I'd have thought it's standard (it's the category of small categories), but I suppose there's some room for ambiguity.

epi: Yep, technical term.

w.r.t.: Fixed.

fact: the fact is in the lemma. I should probably change that to "lemma".

page-breaking: *throws hands up in despair*

equation on page 8: yes, it's meant to be like that, though I'd prefer it to be a bit less ugly.

Random .: You're right, that's not very clear, is it? "." is the name of the binary operation, as in "a.b". I've put a space in after the dot.

Cognoscenti: changed to "2-categorical cognoscenti". FWIW, I didn't know that until ten minutes before I was due to give a talk on what I thought was a new theorem...