Ah, thank you, Angelo! Looks like underscores were suppressed. (I am sure they were in the input.) If this phenomenon is explained somewhere, I would be grateful if someone could provide a link so as to avoid that next time.

I do not understand what is wrong with the LaTeX input. (There is no problem when I compile it.) Please someone tell me or edit the source accordingly, thanks!

Je t'en prie ! (Excuse my French.) I should have made clear that I addressed only the first point (the answer to which is standard), sorry about that. The second one is indeed trickier (see Charles Rezk's answer).

If I am not mistaken, this is the same proof as the one given by Maltsiniotis in "La Théorie de l'homotopie de Grothendieck", page 68 of math.jussieu.fr/~maltsin/ps/prstnew.pdf. He goes on to prove that not only is this category contractible, but this is also a weak test category. You can also have a look at section 1.8 of the document. (This comment may be slightly off-topic, but I thought people interested in this question might be interested to know that.)

"Are there any results where higher categories or the higher categorical perspectives play an essential role?" Higher categories play an essential role in making me thrill. (Although I must admit that this result may be reached by other means.)

@quid: I agree with you. (I thought it was clear from my comments.)

(I once more insist that I do not find this a good question in its current form.) In the eighties, shortly after receiving "Pursuing Stacks", Bénabou ran a seminar in Paris in order to study the content of the text. I do not know what conclusion he drew himself, but I have heard several other participants of the workshop say that they just were not able to get through the difficulties. That nobody has been able to figure how to make a readable text out of the typeset version at the time did not mean nobody would ever be able to achieve that.

If the text was written in 1986, that is about two years after "Pursuing Stacks", and the same year during which some parts of "Récoltes et Semailles" was written, several years before "Les Dérivateurs". Both "Pursuing Stacks" and "Les Dérivateurs" turned out to contain beautiful and important ideas, in spite of their having been neglected for years (at least for the first one) before some people realized it could be turned into something which everybody now find readable. (Even if these texts are not published yet, a part of the content is already available at least through expository texts.)

I do not think this is a good question either, but to comment on quid's statements: "do you think Scharlau did not check back with some other people (in the know) before saying it cannnot be turned into anything readable?" The only way to know would be to ask Scharlau with whom he has discussed this topic, or ask people whom you consider "in the know" whether Scharlau has asked them if the text could be turned into anything readable. Of course, the answer then depends on what you consider to be "readable" and whom you consider to be "in the know".

Dear Ben: I see your point and I agree that your point of view is reasonable, but then I am still slightly unreasonable about that. "Anybody can write anything they want on their CV", right, but I guess no serious department would hire an applicant they do not know on the sole basis of a written CV. If the CV content shows blatant discrepancy with the reality, I think it jeopardizes the candidate's chances to get the job much more than many other things. (At least I would like it to be that way. I confess I have no experience.) But I am getting subjective and argumentative here, sorry.

(continued) also has to interact with students and their colleagues, maybe even talk to them about something else than Mathematics? I know research is mostly a solitary work, but am I a fool to consider that being able to communicate is important too, and that language skills are important to that respect given the internationality of the mathematics community?

Dear Ben: Well, of course the vast majority of mathematicians possess at least basic skills in English nowadays, so I understand no one really cares if the applicant's command of English enables him to teach Basic Calculus or Algebra II. Besides, we probably all know brilliant mathematicians whose mother tongue is almost not spoken abroad and whose ability in English are very poor, yet they would be hired at once by every maths department, and the department of course would be right to do so. But the average mathematician (to be continued)

May I say that the fact that no one seems to pay attention to language skills throws me into despondency?