Can somebody give me a reference to a proof of the following result (or some generalisation of it)? (I need this in my research, and if a proof is published somewhere, I don't have to do the proof myself) Let C be a small category and let F:C -> Set be a functor. Then, the slice category Fun(C,Set)/F is equivalent with Fun(G(C,F),Set) where G is the Grothendieck-construction for Set-valued functors as described in "Category theory for computing science" (Barr and Wells) chapter 11. As a simple example, take C=1, and one becomes the well-known fact that Set/A is equivalent with Fun(A,Set) (A regarded as a discrete category). If this is "well-known" among category-theorists, without any published proof around, please let me know this too. Thanks in advance, Frank Piessens Dept. of Computing Science Katholieke Universiteit Leuven ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++