On the Computation of Certain Weighted Colimits

The present paper gives computations of weighted pseudo-colimits of pseudo-functors on 1-categories valued in certain 2-categories, such as the 2-category of contravariant pseudo-functors on a 1-category. The main result is a generalization of the well-known result of SGA 4 that shows how to compute conical colimits of certain cloven fibrations. Concluding discussions give an computation of bicolimits of certain pseudo-functors and colimits in reflective sub 2-categories.