reserve y for set;
reserve C,D,E for Category,
  c,c1,c2 for Object of C,
  d,d1 for Object of D,
  x for set,
  f,f1 for (Morphism of E),
  g,g1 for (Morphism of C),
  h,h1 for (Morphism of D) ,
  F for Functor of C,E,
  G for Functor of D,E;
reserve o,o1,o2 for Element of commaObjs(F,G);
reserve k,k1,k2,k9 for Element of commaMorphs(F,G);

theorem
  the carrier of 1Cat(x,y) = {x} & the carrier' of 1Cat(x,y) = {y};
