On 23 Jul 2014, at 3:42 pm, Jean Bénabou <jean.benabou@wanadoo.fr> wrote:
In view of this example I suggest that the name of fibrations should be used exclusively for Grothendieck fibrations, the usual ones or their internalizations along the lines I described, and another name, e.g. weak fibrations, be given to the notion defined by Street. Woud you agree with this, Ross ?
Dear Jean Yes, I do agree that ``weak fibration'' or ``pseudo fibration’’ would be good terminology. The ``pseudo-fibres” rather than the strict fibres are the relevant concept. There is no doubt that Grothendieck fibrations are very important. But the pseudo-fibrations do have a mathematical role, as outlined is a message sent to ``categories’’ (by a group of us) a year or two ago. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]