Mathematical Society Summer 2006 Meeting,
Abstract (Joint work with Marcelo Fiore)
In the 1960s, Richard Thompson (and independently, Freyd and Heller) discovered three groups, F, T and V, with several remarkable properties. F, in particular, turns out to be one of those structures that appears unexpectedly in many diverse parts of mathematics. It also has a very natural and simple categorical description: it is the symmetry group of the 'generic idempotent object'. I will explain what this means, how it differs from Freyd and Heller's earlier description, and how it belongs to the large family of existing descriptions of free categories with structure.