Dear Peter I was also a participant at the Oberwolfach 1966 meeeting as you may recall, and heard Lawvere give his lecture. Although I cannot find my own notes, those of Anders Kock bring back my recollection of it. The following is relevant to your comments. I myself gave there a talk about an aspect of my thesis -- namely a characterization of functor categories ("diagrammatic categories") based on what I called "regular categories, a Set-version of your abelian categories, as well as on Bill's idea, expressed in his lecture, that, thinking of the category of ordered sets, the analogue of Sets^{C} is 2^{\Lambda}. This analogue led to the idea of atoms in order to emphasize the analogous characterization of complete atomic Boolean algebras as fields of sets. For the record, my thesis (Marta C. Bunge Categories of Set-valued functors, University of Pennsylvania 1966) was unpublished as such and only parts of it in a different version appeared three years after completion (Marta C. Bunge "Relative Functor Categories and Categories of Algebras" J. Algebra 11-1 1969, 64-101), at the insistence of Saunders Mac Lane, who communicated my paper. About profunctors. My thesis as you may recall contains an entire chapter (III) on equivalences of diagrammatic categories and adjoint functors between them. Theorem 14.1 states that for M any complete category and B a small category Adj(Sets^B M) \equiv M^{B\op}. In particular Adj(Sets^B\, Sets^C) \equiv (Sets^C)^{B\op} \equiv Sets^{B\op x C}. Relevant to this is a previous paper by Michel Andre, Categories of functors and adjoint functors, Batelle Reports, Geneve 1964, which I quote both in my thesis and in the J. Algebra paper. It is furthermore remarked in my thesis that, when I is a discrete category, the statement Adj(\Sets^I \, Sets^I) \equiv Sets^{I x I) has an obvious interpretation analogous to that which exists between endomorphisms of a vector space and matrices. This remark was further expanded (section III.14) into a discussion of the analogue of matrix multiplication for "profunctors". Therefore, although I do not recollect Benabou's lecture or what followed it, Bill's lecture and my own thesis are, for me, enough indication of priority over Benabou's distributeurs. Thanks for giving me this opportunity to comment on a meeting that I had forgotten about. Best regards Marta [For admin and other information see: http://www.mta.ca/~cat-dist/ ]