theorem
 Hom(a,b) <> {} & Hom(b,a) <> {} &
  g*f is retraction implies g is retraction
proof assume
A1: Hom(a,b) <> {} & Hom(b,a) <> {};
  assume
A2: Hom(a,c) <> {} & Hom(c,a) <> {};
  given i being Morphism of c,a  such that
A3: (g*f)*i = id c;
  thus
A4: Hom(b,c) <> {} & Hom(c,b) <> {} by A2,A1,CAT_1:24;
  take f*i;
  thus g*(f*i) = id c by A2,A3,A4,A1,CAT_1:25;
end;
