Remarkable properties of monads related to the semantics of non-determinism
Matias Menni, Universidad Nacional de La Plata
Date and time: Thursday 16th April 2009 at 14:00
Location: UG40, School of Computer Science
Host: Martin Escardo
Let M = (M, m, u) be a monad and let (M A, m) be the free M-algebra on the object A. Assume that the canonical presentation a : (M A, m) -> (A, a) of the algebra (A, a) has a section s : (A, a) -> (M A, m). The retract (A, a) is not free in general. We observe that for many monads with a `combinatorial flavor' such a retract is not only a free algebra (M A0 , m) but it is also the case that the object A0 of generators is determined in a canonical way by the section s. We give a precise form of this property and explain its combinatorial motivation by discussing several examples, among these, compact convex spaces.