  This text is an updated version of material used for a course at Universit\'e
de Nantes, part of `Functor homology and applications', April 23-27, 2012. The
proof by Touz\'e of my conjecture on cohomological finite generation (CFG) has
been one of the successes of functor homology. We will not treat the original
proof in any detail. Instead we will focus on a formality conjecture of
Cha{\l}upnik that leads to second generation proof of the existence of the
universal classes of Touz\'e.
