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this MO question on relative cohomology made me create an entry with an attempt to give the fully general abstract definition in the spirit of the discussion at cohomology
a very stubby note is now at relative cohomology
this clearly needs more development, but I think the basic idea is obvious
For my own part, is only laziness that makes me write something once and in a slick general fashion (although I don't write about these topics). I'm pretty sure that Urs agrees that it's good to give simple explanations accessible to 1-category theorists for the 1-categorial case (in fact, I think that he's already said so somewhere around here). It's helpful if people say what they're particularly interested in seeing a more accessible description of, as Todd recently did on another topic.
Yes, so a general point is that just because I write something in some way does not mean that I don't want to have something else be written. Quite the contrary.
But recall what's going on here, from the HomePage: I am not being paid for running a site that answers other people's needs. If that happens, it's a pleasant side-effect.
Instead, I use the nLab to jot down insights that I need for my own benefit. If now you come along and add your insight, or ask me something or the like, then we get going into a nice win-win situation.
That said, let's be fair, maybe: I believe I and other regulars here are spending already more time on non-selfish tasks than some other people might think is good for us -- if you know what I mean.
Anyway, the punchline is: if you feel an entry doesn't give you what you are looking for but don't feel youare the one to change this: drop query boxes, drop query boxes, drop query boxes.
These boxes will sit their, patiently, and calmly keep asking everyone passing by to react. Eventually somebody will.
right, I understand. But the only way out is if you and others join in and help out.
For instance Eric Forgy, who has been a bit quiet lately, has done a great job pushing accessible expositions at a number of entries. Once somebody wrote something unintelligibly sophisticated, he would start asking concrete questions here, or put query boxes in the entry, or added himself stuff that was clarified in discussion.
This here must be a "community undertaking", as it says on the home page, or it won't work. Myself, and other regulars here, have trouble finding enough hours in the day to do what I really need to do. There is just no way that each time I start writing an entry I try to do it in full textbook glory at once, starting with all the introduction, all the motivating examples, and slowly leading up to some more abstract point of view and so on. But I eventually want this to happen just as much as you do, really.
It can happen, eventually, if everybody who cares joins in and adds his or her contribution. Don't feel shy about going to some unintelligibly abstract entry, and create a new section titled "low-brow-description" or the like. You don't even have to give that low-brow description if you don't feel you actually know what's meant. Just open a green query box and say things like "I suppose this relates to.. and the like". Then we'll all get going on developing this further.
Meanwhile, what happened to the nLab server?
It was down, but now it's back.
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