reserve C for category,
  o1, o2, o3 for Object of C;

theorem Th19:
  for A, B being transitive with_units non empty AltCatStr for F
being covariant Functor of A, B for o1, o2 being Object of A, a being Morphism
of o1, o2 st <^o1,o2^> <> {} & <^o2,o1^> <> {} & a is coretraction holds F.a is
  coretraction
proof
  let A, B be transitive with_units non empty AltCatStr, F be covariant
  Functor of A, B, o1, o2 be Object of A, a be Morphism of o1, o2 such that
A1: <^o1,o2^> <> {} & <^o2,o1^> <> {};
  assume a is coretraction;
  then consider b being Morphism of o2, o1 such that
A2: a is_right_inverse_of b;
  take F.b;
  b * a = idm o1 by A2;
  hence (F.b) * (F.a) = F.idm o1 by A1,FUNCTOR0:def 23
    .= idm F.o1 by FUNCTOR2:1;
end;
