A morphism of pointed sets1,2 is equivalently:
- A morphism of $\mathbb {E}_{0}$-monoids in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathsf{Sets}\webright ),\text{pt}\webright )$.
- A morphism of pointed objects in $\webleft (\mathsf{Sets},\text{pt}\webright )$.
1Further Terminology: Also called a pointed function.
2Further Terminology: In the context of monoids with zero as models for $\mathbb {F}_{1}$-algebras, morphisms of pointed sets are also called morphism of $\mathbb {F}_{1}$-modules.
