reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;
reserve f,f1,f2 for Morphism of a,b;
reserve f9 for Morphism of b,a;
reserve g for Morphism of b,c;
reserve h,h1,h2 for Morphism of c,d;

theorem Th64:
  for T being (Functor of C,D), f being Morphism of C holds (Obj
  T).(dom f) = dom (T.f) & (Obj T).(cod f) = cod (T.f)
proof
  let T be (Functor of C,D), f be Morphism of C;
  T.(id dom f) = id dom (T.f) & T.(id cod f) = id cod (T.f)
          by Def19;
  hence thesis by Th62;
end;
