Dear Jean, this mail is a valuable contribution to the subject. Concerning your last comments about crediting it, I suggest you put a title like "Comments on fibrations and foliations" or any other of the sort, and you upload it to the arXiv. In this way, it will have a wider distribution (its interest is not limited to this list) and even it will be possible to put it in the references of any paper and book if the author has a fair perception of your contributions. best regards e.d. On 28/07/14 06:54, Jean B?nabou wrote:
Dear Ross, Dear all,
In a recent mail I asked Ross if pseudo cartesian functors between pseudo fibrations had been studied. There are many generalizations of fibrations. Pseudo fibrations are only one of them. But there are also prefibrations, defined by Grothendieck, but almost never considered, and pre foliations, which I define here, which generalise greatly pre fibrations. For such pre foliatons, I define cartesian functors and show that they have striking properties, most of which are not known, even in the very special case of fibrations. I thought this brief survey might interest you, in case you decide to study seriously the properties of pseudo cartesian functors.
Best regards to all, Jean
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