reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem
  for cd being Object of [:C,D:] ex c being Object of C, d being Object
  of D st cd = [c,d] by DOMAIN_1:1;

definition
  let C,D;
  let f be Morphism of C;
  let g be Morphism of D;
  redefine func [f,g] -> Morphism of [:C,D:];
  coherence
   proof
    thus [f,g] is Morphism of [:C,D:];
   end;
