
theorem Th1:
  for A,B being transitive with_units non empty AltCatStr, F
being covariant Functor of A,B for a being Object of A holds F.idm a = idm (F.a
  )
proof
  let A,B be transitive with_units non empty AltCatStr, F be covariant
  Functor of A,B;
  let a be Object of A;
  <^a,a^> <> {} & <^F.a,F.a^> <> {} by ALTCAT_2:def 7;
  hence F.idm a = Morph-Map(F,a,a).idm a by FUNCTOR0:def 15
    .= idm (F.a) by FUNCTOR0:def 20;
end;
