LII - 4 , 4 ème trimestre 2011 SOMMAIRE

We show the existence of bilimits of 2-cofiltered diagrams of topoi, generalizing the construction of cofiltered bilimits developed in [2]. For any given such diagram represented by any 2-cofiltered diagram of small sites with finite limits, we construct a small site for the bilimit topos (there is no loss of generality since we also prove that any such diagram can be so represented). This is done by taking the 2-filtered bicolimit of the underlying categories and inverse image functors. We use the construction of this bicolimit developed in [4], where it is proved that if the categories in the diagram have finite limits and the transition functors are exact, then the bicolimit category has finite limits and the pseudocone functors are exact. An application of our result here is the fact that every Galois topos has points [3].