  Lusztig proved the compatibility of induction functors and restriction
functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a
categorification of Green's formula and gave a sheaf-level proof of this
compatibility for all semisimple complexes. As an application, we study the
relation between induction functors and derivation functors, which is a kind of
special restriction functors.
