We report on progress on a functorial approach to decision problems, making some remarks on how one may define these to be shaves on suitable sites, and the consequences that this has. Some minor results are given (without proofs) but otherwise this is just a synthetic report about work in progress.

I am chargé de recherche (resarcher) at CNRS, working at the Laboratoire d’Informatique de Paris Nord, Université Paris 13. I’ve held this position since 2008. Previously, I was post-doc at Preuves, Programmes et Systèmes and at LIPN. I did my Ph.D. thesis (which I defended in 2006) at the Institut de Mathématiques de Luminy, in Marseille. Before that, I studied CS Engineering in Rome, Italy (which is where I am from).