The category of pointed sets is the category $\mathsf{Sets}_{*}$ defined equivalently as
- The homotopy category of the $\infty $-category $\mathsf{Mon}_{\mathbb {E}_{0}}\webleft (\mathrm{N}_{\bullet }\webleft (\mathsf{Sets}\webright ),\text{pt}\webright )$ of
; - The category $\mathsf{Sets}_{*}$ of .
