Canonical lcn_gFun n := [gFun by lcn_cont n].
Canonical lcn_mgFun n := [mgFun by fun _ G H => @lcnS _ n G H].
Section UpperCentralFunctor.
Variable n : nat.
Implicit Type gT : finGroupType.

Lemma injm_nil G : 'injm f -> G \subset D -> nilpotent (f @* G) = nilpotent G.