Marta Bunge (McGill University) Distribution Algebras ABSTRACT The purpose of this talk is to report on some recent work on lattice theoretic aspects of S-valued (Lawvere) distributions on an S-bounded topos E. The main result is a duality between the category Dist(E) and the category of S-bicomplete S-atomic Heyting algebras (or "distribution algebras") in E. Closely related with this duality is a relativization of the Pare tripleableness theorem involving a double power set triple. Concretely, we show that Dist(E) is an E-category with a cogenerator o = e^*(Omega_S).1 (where 1 is the terminal S-valued distribution on E), and that the adjoint pair o^(-) -| HOM(-,o): (Dist(E))^op---->E is tripleable. We also examine, in terms of distribution algebras, the passage from distributions on E to complete spreads over E. (This is joint work with Jonathon Funk (UBC), Mamuka Jibladze (Tbilisi) and Thomas Streicher (Darmstadt).