Le localisateur fondamental minimal, by Denis-Charles Cisinski

We show a conjecture stated by Grothendieck in "Pursuing stacks" about the homotopy theory of small categories. This gives a caracterization of the weak equivalences defined by the classifying space functor as the smallest class of arrows satisfying simple stability conditions. Furthermore, we give another caracterization of these weak equivalences inspired by Quillen's theorem B.

Denis-Charles Cisinski <cisinski@math.jussieu.fr>