
theorem
  for C being Category, a,b being Object of C, f being Morphism of C st
f in Hom(a,b) holds Den(compsym(a,b,b), MSAlg C).<*id b, f*> = f & Den(compsym(
  a,a,b), MSAlg C).<*f, id a*> = f
proof
  let C be Category, a,b be Object of C, f be Morphism of C;
  assume
A1: f in Hom(a,b);
  then dom f = a by CAT_1:1;
  then
A2: f(*)id a = f by CAT_1:22;
  cod f = b by A1,CAT_1:1;
  then
A3: (id b)(*)f = f by CAT_1:21;
  id b in Hom(b,b) & id a in Hom(a,a) by CAT_1:27;
  hence thesis by A1,A3,A2,Th31;
end;
