Hi, The following paper is very clear, I'm currently learning the basics of the subject with it: http://people.math.jussieu.fr/~maltsin/ps/ asphbl.ps. It's written in French. Another member of this mailing- list has asked me to translate it in English, I may be able to send you a rough translation in a few weeks. Best, Jonathan Le 15 avr. 09 à 15:45, Hasse Riemann a écrit :
Hi category gurus and categorists
I have many questions about category theory but i start with one.
1>
What are smooth functors and proper functors, originating in pursuing stacks?
Both nontechnically and technicaly.
I know they are dual to each other and that they are characterized by cohomological properties
inspired by the proper or smooth base change theorem in algebraic geometry, but what is the relation?
(I don't know the statement of the theorems)
Finally, what are smooth and proper functors good for?
Are smooth and proper functors fibrations and cofibrations or Grothendieck fibrations and
Grothendieck op-fibrations in some model categories or derivators?
The only thing i could find about smooth and proper functors on internet is the last entrance in http://golem.ph.utexas.edu/category/2008/01/ geometric_representation_theor_18.html
Best regards
Rafael Borowiecki