  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.
