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There is a workshop called "Catégories supérieures, polygraphes, homotopie" in Paris: pps.jussieu.fr/gdt-h-ncat. I have listened to many talks related to these questions there. People are welcome.
Dear Will: Thanks for the explanation. Actually, there are similar pairs of words in French, and "inspiré" is slightly overused too, in the same fashion (as far as as I can tell) as in English. However, I am unsure as to how people would understand a sentence such as "Je suis expiré". I will have to try it some day.
Are you expired or inspired? (This is a real question, designed to improve my understanding of English vocabulary as well as your current condition. Sorry for the off-topicness.)
Ah, thanks! I'm abroad for a few weeks and cannot look it up now. I'll check that when I'm back. Besides, before seeing your answer, I thought I would answer my question myself because Bénabou told me last month that this coherence result was a special case of a quite general result in his thesis, which should have been published but, for some reason unknown to him, was not. I'll write about that as soon as I find the proper reference.
It would be useful for me if a new tag "2-category-theory" (where specific questions arise which belong neither to "higher algebra" nor "category theory" as most people understand these terms) was created. I think some other people may use it sometimes too. But I have not been able to find rules to abide by when creating a new tag.
Thanks! It is basically what I had in mind, at least for the first two items. The third one is interesting. If I am not mistaken, your answer illustrates the fact that a lax transformation between two strict 2-functors from \mathcal{A} to \mathcal{B} gives a lax functor from \Delta_{1} \times \mathcal{A} to \mathcal{B}, but that the converse is false because the cartesian product with \Delta_{1} does not coincide with the Gray tensor product with \Delta_{1}. Am I right on this point?
People may point out that, given the pieces of information provided in my profile, I should work this out myself. The answer is that I will if nobody has done it before, but that I would be glad not to do it if the results are already known or even written down somewhere.
I'm unsure as to how I could use his results for the concrete case I have in mind, I'll have to take a closer look, but thanks anyway, I wasn't aware of this work.
I don't know, but I just want to point out that I have yet to meet someone able to explain to me what is the Gray tensor product in $2-Cat$ in terms which could make me work with it, so I wish you good luck with its \omega-Cat analog
Thanks! I am aware of the Quillen equivalence which you mention, but I fail to see right now the details as to how it lifts to an equivalence between $2-Cat$ and the category of simplicial categories. When I saw your comment I first thought there was some result of which I was not aware, stating that a Quillen equivalence could be lifted up to the level of enriched categories under some assumptions, but as far as I know there is no known model structure on $2-Cat$ whose weak equivalences are Dwyer-Kan equivalences, so I am probably really missing something, and I am afraid it may be obvious.
