Dear categorists, I have three questions, the first one is a mathematical question, the second one a bibliographical question and the last one is a speculative question. 1) Let K be a complete, cocomplete and cartesian closed category. Consider the category DK of all small diagrams over K. The objects are all small diagrams F:I-->K from a small category I to K. And a map from (F:I-->K) to (G:J-->K) is a functor f:I-->J together with a natural transformation mu:F-->Gf. DK is complete and cocomplete and I would like to know if it is cartesian closed as well. 2) My question was initially posted in https://mathoverflow.net/q/266597/24563. From MathOverflow, I now know that the functor DK-->Cat forgetting K is a fibred category. Since then, I browsed the Borceux book's chapter devoted to fibred categories (Vol.2 Chap.8). Is there other reference you could recommend me ? 3) I also would like to know what is known about the link between locally presentability and fibred category. Googling these terms or looking them up in MathSciNet together gives nothing relevant. Actually, my motivation is to know whether D(DeltaTop) and D(SimplicialSet) are locally presentable and cartesian closed (DeltaTop is the category of Delta-generated spaces, and SimplicialSet the category of simplicial sets). Therefore I would like to conclude this email with a speculative question: is there a general philosophy to deduce from the properties of the fibers of a fibred category E-->B the same property on E ? In the case of DK-->Cat, the fiber over I is the well-known category of I-shaped diagrams over K... Philippe Gaucher. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]