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there is some confusion on this MO thread about sheafification, with the $n$Lab entry sheafification somehow involved. I had a look at the entry and find that it can do with lots of polishing, but that the statement discussed over there is clearly right. (the misleading answer on MO that seems to claim a problem on the nLab page gets twice as many votes as the good answer by Clark Barwick, which confirms the statement) I have tried to edit it a bit to make things clearer, but don’t have the leisure for that now.
Given the recent success with the polishing of the entry on geometric realization, maybe I should announce that sheafification is going to be submitted for $n$Journal peer-review soon, so that everybody here will jump on it to brush it up ;-)
Though you said it in a joke manner, let me anyway comment that I do not think that an inhomogeneous stub entry of this kind should be in nJournal, rather that some parts could have some mark on proof as you had an idea before. :)
I do not think that an inhomogeneous stub entry of this kind should be in nJournal,
I think they should be eventually turned into homogenous comprehensive entries and then be subitted to the $n$Journal.
If that MO discussion shows one thing, then it is the need for decent $n$Lab material on these basics. It hurts me to see what’s going on here, but I don’t have the time to do anything about it right now.
I think nJournal should have either original research or specific surveys (or some other similar categories). The regular pages of nLab could have reviewed theorems or alike, but choosing some moment as special and declaring this is a moment when I want the WHOLE big standard entry reviewed means that the contributions just before that are more appreciated than just after that. This is kind of a pressure which foreseeing would be very demotivating at least for me. I know that the reviewed things can be expanded later, but now we are again coming at the discussion we had few months ago. And we agreed then that it is good to review meaningful exact parts like theorems, definition, I also agree articles of specific, personal or review nature. But just a concept entry like sheafification, have reviewed in somebody’s moment of hapiness, no I don’t think it is a good idea. For example, I could be happy with such an entry only if it had good treatment of sheafification with values in other categories, and also in noncommutative context. I do not believe this is a wish of other people in nLab. So why would somebody put the will and have it revwied in a moment which other may consider a stub phase ? on the oter hand, everybody may be happy with previous idea of reviewing for correctness some theorem and alike. But reviewing for the nJournal is not a limited reviewing just for correctness or what somebody chooses to review. It should be a comprehensive overall judgement; hence it is not appropriate for an ever growing open end concept page but for limited reviews as well as original research in my opinion. I feel depressed hearing that it will get reviewed when some contributor decides. Edit: Though in some moment somebody can choose to extract an adaptation of his own. So one can choose to submit Urs-extract-sheafification-1 and have that reviewed as a whole in a special section of nLab.
Finally, massive perpetual tasks of checking and approving aspects of particular theorems and so on, which can have many reviewers including self-appointed referees is a bit different from an assignment of official referees by a small group of busy editors. We were talking on massively multiply and forever checking of parts of the entries once the software grows into that few months ago; now we have here a journal model which does have some similarity to this but still has submittance phase and definite acceptance phase which is finite in time. The two kinds of checking, massive perpetual and partial versus strictly itemized, editor-driven and finite in time really deserve different software and means. For the latter editorial type we need less specific software so can proceed even earlier. I mean reviewed nLab content versus nJournal. I am for both and many more, but should be separated. Reviewed nLab content may not need to ever be separated from main nLab, provided we had few software tools to mark the things. nJournal is already separate.
I agree with Zoran #4; I’m not all that comfortable with the idea of extracting and freezing “snapshots” of lots of individual pages.
I have trouble seeing the problem. If somebody comes along and says, “hey, I am Mr. ToposBigShot and I officially declare that this page in version xyz looks good to me, you may quote me on that”, then I can’t see any harm of recording that fact by putting that version with that referee signature on the $n$journal-web. it adds value to the page and harms nobody.
Urs, you seem did not read what I wrote. I clearly wrote that voluntary approvals of some aspects opf theorems, pages, proofs are welcome and that we need to develop software making this possible. I am repeatedly saying that there is a distinction between
an appointed, quantized and complete refereeing of entire article from true referees certified by editorial board as competent from
the massive and partial tasks of virtually thousands of partial approval comments by non-appointed “referees”.
For example, saying “a proof is correct” which adds value to a page is not a complete review of a page/paper or whatever which makes it accepted. Why going on with an external board if one is not to distinguish appointed and certfied referees of entire work from all aspects (not only impression of correctness) from the partials ? Most of people here see the difference, it startles me that you wrote 7 as if there were no clarifications about the distinction (including in bold letters “massive perpetual and partial versus strictly itemized, editor-driven and finite in time”).
On the other hand, what do you see troublesome in having delimited categories of various kinds of contributions ? (I am talking at least 2 categories now: comments/approvals of quality of items in the main nLab with added software and separate nJournal appointed complete refereeing of entire articles; the first category would suffice and be more appropriate for sheafificationand hundreds of other items, and be partly and gradually stamped in the moments of leisure of volunteers, without need of editorial board to bother with such low level stuff)
the massive and partial tasks of virtually thousands of partial approval comments by non-appointed “referees”.
This is something that does not exist has not been planned and is unlikely to make sense. I am not sure where you get this from.
Instead of discussing hypothetical and increasingly unlikely potential problems, let’s use our energy to make small steps towards making things exist. For instance to make the entry sheafification nicer! :-)
Urs, you wrote:
Suppose Zoran writes out a proof on some nLab page. Somebody finds the result interesting and would like to cite it. But since it is not journal-published, it does not carry the stamp “passed through peer-review”, so won’t be considered citable. But suppose now there is a small remark there saying that Mike and Todd looked at the proof and found it to be correct. Then that makes the theorem have peer-review status (even considerably better one than the traditional journal peer review).
That would greatly improve the value – scientific-community-wise – of Zoran’s effort of writing up that proof on the nLab. In fact, as soon as there is some record of such peer-reviewed statements on a wiki, I could easily imagine that we get to the point where Zoran need not go and send that theorem to some random editor who will pick some random referee who with a random chance is able to verify that theorem. Instead, people will point to the nLab and say: look I am using this theorem verified by Skoda, Shulman and Trimble.
Instead of discussing hypothetical and increasingly unlikely potential problems
If somebody is seeing the problems with having more than one category it is you. What is nonsensical about approving particular theorems ? You wanted few months ago to have a system which will codify the format of particular theorems to allow some sort of, hard to achieve, indexing system. I think it is much easier to have indexing and storage of (validity and other quality) comments attached to each proposition, theorem or proof. This is independent from rambling ideas sections, additional chapters in an entry etc. We were discussing (and you agreed) about various levels of approval like “I have read this page and it looks reasonable to me”, “I have read this proof and it sounds correct to me” etc. Neither of such comments is overall complete approval by an appointed referee certified for competence by an editorial board but are just partial efforts by volunteers. It is strange that you do not see that for volunteers it makes no sense to employ editors; every partial comment should be welcome in all sections of nLab, submitted or not! If I decide to spend my time checking some proof, why would I wait for the status of submitted entry, or wait other section of a stub to be written ? I can do that when I study particular subject, not asking or bothering any board. That makes sense to me. On the other hand, if we want to give somebody an official task of checking the whole submission, than we need an editorial board, we need the guy to take full responsibility, the guy’s identity and comptence need to be cerfitified by the authority of the board and one needs to make sure that authorities checked all aspects in reasonable degree of reliability. This is a different procedure and there are different expectations. (For example, after hearing the idea that two mix I gave up the idea I had up to yesterday to submit one of my articles from arxiv to the nJournal. If the delimitations are not known I am not interested.)
By the way, while i am for further development of software and practices of certification, with more than one possible and encouraged mode, I also think that in principle I see no problem in quoting noncertified nLab pages in articles, possibly with a date of last edit, as arxiv papers are cited, sometimes with version.
What is nonsensical about approving particular theorems ?
Nothing, I think. We all seemed to have agreed on that. It is part of the project description at Proceedings preparation (nlabmeta).
It is strange that you do not see that for volunteers it makes no sense to employ editors;
On the contrary, that is part of my whole motivation for this project: we want transparent refereeing and if somebody coms along and says “I have checked this theorem” then this would be something to put on what is now called (maybe misleadingly) the $n$Journal.
If I decide to spend my time checking some proof, why would I wait for the status of submitted entry, or wait other section of a stub to be written ?
I think you wouldn’t have to wait. Just submit the proof!
I think you wouldn’t have to wait. Just submit the proof!
I am not taking about writing a proof. I am talking about checking Mike’s proof, partly written by Todd, which is now in an entry which will not be finished until 2013. “I want to stamp that particular proof to say I read it (and not the rest of the entry) and approve it for correctness” It is not about making prematurely the entry from 2013 to the attention of some editorial board or alike.
It is part of the project description at Proceedings preparation
You are saying there one can isolate a theorem and publish it standalone. It does not always make sense isolating something from the context. I am saying what is wrong about an entry staying somewhere in the middle of the page, just adding a flag to it: I, Zoran, have reviewed this particular proof and checked it for correctness. I see no reason to have announcement of submission to some board for doing that. I just need some very minor addition to the software to be able to store some sort of flag entry or link to a special section of nForum containg such certificates.
if somebody coms along and says “I have checked this theorem” then this would be something to put on what is now called (maybe misleadingly) the nJournal
Urs, it is far far less energy and far less asking from the community if I just fill in few seconds a line like
REVIEW FLAG(Zoran Škoda) I read this proof and find it correct. END OF FLAG
than to edit a new page, extract a theorem from the context to a new page, write the silent assumptions from the entry to that entry, and contact and bother the editorial members that I want to consider this extracted theorem in my editing to be submitted. Especially if the proof has been written by Mike than I do not want to initiate its submission. I just want to flag it, because I am now working on that subject and as a part of my routine I read in that area and in particular I read and chekd Mike’s proof.
I think you wouldn’t have to wait. Just submit the proof!
I am not taking about writing a proof. I am talking about checking Mike’s proof, partly written by Todd, which is now in an entry which will not be finished until 2013. “I want to stamp that particular proof to say I read it
Yes, I know. And you can submit it. We have explcitly that statement about “third-party submissions” at Proceedins preparation (nlabmeta) meant to precisely allow this situation.
It does not always make sense isolating something from the context.
Sometimes it will, sometimes not. Clearly the smallest bit subject to any review is one that is minimally self-contained. Should we say that more explicitly in the entry? I’d think that’s clear.
I just need some very minor addition to the software
Right, this is what I had proposed originally. But it was not going to happen. So now we try something that is going to happen.
You see, in ideal software, every theorem which has at least one flag could have a link “Flags” (rather than comment boxes all around) which would lead to a nForum or other mini-page containing all the flags. The name of the contributor of a flag and the date of the flag should be listed automatically with the submission of that flag (this immediately gives a version control). This way, items within normal nLab pages would accumulate by a very natural process flags of various quality through lifetime.
Right, this is what I had proposed originally. But it was not going to happen.
I am telling you, let’s propose both and many more sections. I think it will happen. Maybe even I myself write a software, once when I get a permanent contract (this may be in a year or less). The idea with a special section of nForum for flags is for example easy. And the whole thing is 2 orders of magnitude easier than the system of indexing all theorems by concept which you proposed at some point.
It is still not clear what is the role of editorial board.
Yes, I know. And you can submit it. We have explcitly that statement about “third-party submissions” at Proceedins preparation (nlabmeta) meant to precisely allow this situation.
Yes, I can, but it is unlikely that I will want. Submission is about all aspects, not just about correctness or any particular aspect one wants to flag a theorem in particular moment. The Proceedins preparation (nlabmeta) is much more complicated than just writing a line saying “I read the proof and find it correct”. If something requires an order of magnitude more effort, needs assistance of others, needs an external editorial board, then forget it, most of the time, when it is about a minor approval, one will not go for it. And our daily nLab routine consists of hundreds of very minor actions, not about one weekly huge completion and approval. Maybe you do more of the latter, so why not, go on for it. But saying other thing won’t happen and labelling my ideas as “discussing unlikely potential problems” is sort of ignorance and is discouraging of a potential where some including me would contribute much more. Should I start hacking labels like
BEGIN FLAG (ZŠ) ahsugfuha END FLAG
to prove that it will happen or there will be a more systematic way encouraged by you as well ? (in particular I think that “FLAGS” should be an optional entry which is a part of a proof environment)
Alternatively I could ask Andrew if he finds it reasonable to open a new section of nForum called “flags” (or badges or approvals…). Each discussion/thread in flags should be backlinked from a single entry or a single theorem-proof environment. Each approval to a particular theorem or entry should be one of the comments in the flags entry linked from that entry or theorem.
Regarding the original topic of this thread, I think that the phrase “is locally isomorphic to” is what caused the confusion, and even with the parenthetical I think it is still potentially confusing. I changed it to “admits a local isomorphism to” which I think is less likely to confuse.
Let’s continue the digression about the nJournal here.
I have now spent a bit time on the entry sheafification, trying to make it comprehesive and polished.
I am almost done, only wanted to add more details where the plus construction is mentioned. But I am being interrupted now.
Thanks! I’d appreciate more details about the relationship of this description to the plus construction too. I gather that somehow taking the colimit-completion of W throws in all the hypercovers as well? Also, the Proposition seems to be missing a proof that the functor L thus defined actually takes values in sheaves.
I gather that somehow taking the colimit-completion of W throws in all the hypercovers as well?
I had started writing out an argument for that, but I am not happy yet.
Also, the Proposition seems to be missing a proof that the functor L thus defined actually takes values in sheaves.
This follows from general facts about reflective subcategories. To make this clearer, I have now added the following to the beginning of that proof:
Now we invoke the following results:
The localization proposition says that every full subcategory of a locally presentable category on the $W$-local objects for a small set $W$ of morphisms is a reflective subcategory, given by the localization at these morphisms;
By Gabriel-Zisman’s theorem every reflective subcategory is the localization at the collection of morphisms inverted by the left adjoint (which by the localization proposition is the saturation of the original set of morphisms).
If $W$ satisfies the axioms of a calculus of fractions then, by the discussion there, this localization is equivalently given by the category $PSh(C)[W^{-1}]$ whose objects are those of $PSh(C)$ and whose morphisms are given by $PSh(C)[W^{-1}](X,A) \simeq {\lim_{\to}}_{\hat X \stackrel{w \in W}{\to} X} PSh_C(\hat X,A)$.
[I see I can polish this further, but have to run now. More later.]
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