• Unitality. We have isomorphisms of pointed sets
    \begin{align*} \webleft (\text{pt},\star \webright )\times \webleft (X,x_{0}\webright ) & \cong \webleft (X,x_{0}\webright ),\\ \webleft (X,x_{0}\webright )\times \webleft (\text{pt},\star \webright ) & \cong \webleft (X,x_{0}\webright ), \end{align*}

    natural in $\webleft (X,x_{0}\webright )\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$.


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