{ obj := fun M => AddSemigrp.of ↑M, map := fun {X Y} f => AddSemigrp.ofHom ↑(AddMonCat.Hom.hom f),
        map_id := AddMonCat.hasForgetToAddSemigroup._proof_1,
        map_comp := @AddMonCat.hasForgetToAddSemigroup._proof_2 }.comp
    (CategoryTheory.forget AddSemigrp) =
  CategoryTheory.forget AddMonCat