CommMonCat.fullyFaithfulForgetToMonCat =
  { preimage := fun {X Y} f => CommMonCat.ofHom (MonCat.Hom.hom f),
    map_preimage := @CommMonCat.fullyFaithfulForgetToMonCat._proof_1,
    preimage_map := @CommMonCat.fullyFaithfulForgetToMonCat._proof_2 }