Thanks. I was not aware of the notion of "convenient topological spaces" as defined at the nLab. But I am curious whether you can really show that the two conditions you mention are necessary for the geometric realization functor to preserve pullbacks.

Thanks. It shows that the Wikipedia entry is false, by the way.

Why do people post relevant answers as comments? The question is asking for a big list, so there isn't anything wrong with one sentence answers.

Sorry for the previous lack of paragraph breaks. I have trouble with the preview mode. I hope it is more readable now.

One can also dream of a notion of x-category for any real (or whatever) number x.

I think it should be checked whether someone in sci.physics "recognised" the reasoning as being like that of a physicist, someone in sci.computer.science "recognised" it as being like that of a computer scientist, &c.

Perhaps I should have added that this story is told at the beginning of "Récoltes et Semailles".

The way I understand timur's comment is that Yoneda's name should begin with a capital letter. But given that his own monicker has none, I am unsure…

Dear Akhil: You're welcome. I had trouble inserting the diagram to state Theorem A, but the relative case is one of the axioms for basic localizers, so you'll find it in Maltsiniotis's and Cisinski's books.

Dear Tim: Thanks a lot for your comment. I have edited my answer accordingly.

@Olivier : C'est Pierre Bergé qui a vendu sa tête de veau aux enchères, pas Pierre Berger.