reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th97:
  for o being object holds not 1Cat(o,U) is U-locally_small
  proof
    let o9 be object;
    set C = 1Cat(o9, U);
    1Cat( o9,U) = CatStr(# {o9},{U},U:->o9,U:->o9,(U,U):->U #)
      by CAT_1:def 11;
    then reconsider a = o9 as Object of C by TARSKI:def 1;
    the carrier' of C c= Hom(a,a) by CAT_1:11;
    then
A1: Hom(a,a) = the carrier' of C;
    C is non U-locally_small
    proof
      assume C is U-locally_small;
      then Hom(a,a) is U-set;
      then {U} is Element of U by A1,COMMACAT:3;
      then U in U by Th18;
      hence thesis;
    end;
    hence thesis;
  end;
