19 April 2005 4:00 - 5:30 Nicola Gambino Title: From distributive laws to pseudo-distributive laws. Abstract: It is a familiar idea that the monad on the category of sets and functions whose algebras are commutative monoids can be extended to a monad on the category of sets and relations. One explanation for this fact follows from the theory of distributive laws. I will describe a two-dimensional analogue of the above result and give an explanation for it in terms of pseudo-distributive laws. The two-dimensional result involves replacing sets with categories, monoids with monoidal categories, and relations with profunctors. There are at least two motivations to consider this: one derives from Winskel's theory of concurrency, and the other from Joyal's theory of combinatorial species.