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

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


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