A pointed set1 is equivalently:
- An $\mathbb {E}_{0}$-monoid in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathsf{Sets}\webright ),\text{pt}\webright )$.
- A pointed object in $\webleft (\mathsf{Sets},\text{pt}\webright )$.
1Further Terminology: In the context of monoids with zero as models for $\mathbb {F}_{1}$-algebras, pointed sets are viewed as $\mathbb {F}_{1}$-modules.
