theorem Th22:
  f is retraction implies f is epi
proof assume
A1: Hom(a,b) <> {} & Hom(b,a) <> {};
  given g such that
A2: f*g = id b;
  thus Hom(a,b) <> {} by A1;
  let c be Object of C such that
A3: Hom(b,c) <> {};
  let p1,p2 be Morphism of b,c;
  assume
A4: p1*f = p2*f;
  thus p1 = p1*(f*g) by A3,A2,CAT_1:29
    .= (p2*f)*g by A3,A1,A4,CAT_1:25
    .= p2*(f*g) by A3,A1,CAT_1:25
    .= p2 by A3,A2,CAT_1:29;
end;
