A morphism of pointed sets1,2 is equivalently:
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A morphism of $\mathbb {E}_{0}$-monoids in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathsf{Sets}\webright ),\mathrm{pt}\webright )$.
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A morphism of pointed objects in $\webleft (\mathsf{Sets},\mathrm{pt}\webright )$.
- 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.
