reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th8:
  for F being Functor of [:A,B:],C, a being Object of A, b being
  Object of B holds (F?-a).b = F.[a,b]
proof
  let F be Functor of [:A,B:],C, a be Object of A, b be Object of B;
  thus (F?-a).b = (Obj F).(a,b) by CAT_2:37
    .= F.[a,b];
end;
