  We uncover several general phenomenas governing functor homology over
additive categories. In particular, we generalize the strong comparison theorem
of Franjou Friedlander Scorichenko and Suslin to the setting of Fp-linear
additive categories. Our results have a strong impact in terms of explicit
computations of functor homology, and they open the way to new applications to
stable homology of groups or to K-theory. As an illustration, we prove
comparison theorems between cohomologies of classical algebraic groups over
infinite perfect fields, in the spirit of a celebrated result of Cline,
Parshall, Scott et van der Kallen for finite fields.
