The category of monoids on $\smash {(\mathsf{Sets}_{*},\wedge ,S^{0})}$ is isomorphic to the category of monoids with zero and morphisms between them.
The category of monoids on $\smash {(\mathsf{Sets}_{*},\wedge ,S^{0})}$ is isomorphic to the category of monoids with zero and morphisms between them.