reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem
  for a,b,c,d being Object of A st Hom(a,b) meets Hom(c,d) holds a = c & b = d
proof
  let a,b,c,d be Object of A;
  assume Hom(a,b) meets Hom(c,d);
  then consider x being object such that
A1: x in Hom(a,b) and
A2: x in Hom(c,d) by XBOOLE_0:3;
  reconsider x as Morphism of A by A1;
A3: cod x = b by A1,CAT_1:1;
  dom x = a by A1,CAT_1:1;
  hence thesis by A2,A3,CAT_1:1;
end;
