Dear all, I'm sure the following observation has been made before. Hopefully, somebody can provide a reference. Many thanks in advance Uwe Wolter *************************************************** We consider a small category B and an element M:B --> Set of the functor category Set^B. By G(B,M) we denote the category obtained by the Grothendieck construction with objects (x,b) where b is an object in B and x an element in the set M(b). G(M):G(B,M) --> B is the corresponding split discrete obfibration. Composing G(M)^op with the Yoneda embedding Y:B^op --> Set^B gives us a diagram in Set^B with shape G(B,M)^op. The observation is that M is the colimit of this diagram where for each (x,b) in G(B,M) the projection p(x,b):B(b,_) ==> M is the natural transformation determined, according to the Yoneda lemma, by the element x in the set b. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]