In June 2000 Jean Benabou gave a course on Distributors at Work of which I prepared lecture notes that were proof read by him and finally accepted in the form as you can find them at http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/DiWo.ps.gz The aim of this course was not to give the latest results but rather to give a most understandable introduction. Nevertheless, one can find there quite a few elementary facts which are probably not so well-known (as e.g. the correspondence to comma and cocomma categories). In the final section of these notes one can also find an outline of Benabou's work on generalised fibrations, i.e. normalised lax functors from B^op to the bicategory of distributors. ----------------------------------------------------------------------------- I use this opportunity also for pointing your attention to my lecture notes for a course on Fibred Categories `a la J. B'enabou which are based on a series of lectures I gave in Spring 1999 on the occasion of a Spring School organised by the PhD Programme "Logic in Computer Science" (for further information about that event look at http://www.pst.informatik.uni-muenchen.de/spring-school99). These lecture notes can be obtained from http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/fib.ps.gz Since the time of the course I have been working occasionally on extending the course notes so that they cover a lot of the topics presented in B'enabou's course on Fibred Categories in Louvain-la-Neuve in 1980. However, in contrast to J.-R. Roisin's hand-written lecture notes of the Louvain-la-Neuve course my lecture notes do not follow any particular course given by Benabou though I am certain that all of the material is due to him. I just have tried to collect in one place most of the facts about fibred categories that I met over the years. I deliberately have excluded the connections with categorical logic and semantics of type theory as can be found in Bart Jacob's encyclopedic book from 1999 published by North Holland. Instead I have devoted some part of the notes to a fibrational understanding of geometric morphism as can be found in the unpublished These of J.-L.Moens from 1982 (clearly influenced by and strongly using the results of Benabou's 1980 course in Louvain-la-Neuve). This aspect is also explained in detail and developed further in Part B of PTJ's "Sketches of an Elephant" (as far as I know). My lecture notes are not too polished, I fear, and haven't been proof read by other people. Nevetheless, they might be useful in providing information which is difficult to access otherwise. Thomas Streicher
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Thomas Streicher