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