theorem
  for T being Functor of C,D st f is retraction holds T/.f is retraction
proof
  let T be Functor of C,D;
  assume
A1: Hom(a,b) <> {} & Hom(b,a) <> {};
  given i being Morphism of b,a such that
A2: f*i = id b;
  thus Hom(T.a,T.b) <> {} & Hom(T.b,T.a) <> {} by A1,CAT_1:84;
  take T/.i;
  thus (T/.f)*(T/.i) = T/.id b by A1,A2,Lm1
    .= id(T.b) by Lm2;
end;
