# Cartesian functors and foliated categories

- 14:00 6th May 2011 ( week 1, Trinity Term 2011 )Lecture Theatre B, Computing Laboratory

In 1961 Grothendieck defined cartesian functors between prefibered and fibered categories. Since then they have been studied only in the case

of fibrations. I shall give a general definition covering many other situations, which reduces to the classical one in the previous cases, and give many important examples of the more general situation.

I shall prove for such functors many results which were not known even in the "classical" situation. Some of these results need assumptions, much weaker than fibrations, which I call prefoliations and foliations which I shall introduce and study briefly. Again many significant examples shall be given.

Although distributors are underlying many such situations I shall keep things "elementary" and use this "tool" very little. Whatever is needed shall be briefly recalled.