Computing Weighted Colimits

Abstract

A well-known result of SGA4 shows how to compute the pseudo-colimit of a category-valued pseudo-functor on a 1-category. The main result of this paper gives a generalization of this computation by constructing the weighted pseudo-colimit of a category-valued pseudo-functor on a 2-category. From this is derived a computation of the weighed bicolimit of a category-valued pseudo-functor.