• Preservation of Colimits. We have an equality of sets
    \[ R_{*}\webleft (\bigcup _{i\in I}U_{i}\webright )=\bigcup _{i\in I}R_{*}\webleft (U_{i}\webright ), \]

    natural in $\webleft\{ U_{i}\webright\} _{i\in I}\in \mathcal{P}\webleft (A\webright )^{\times I}$. In particular, we have equalities

    \[ \begin{gathered} R_{*}\webleft (U\webright )\cup R_{*}\webleft (V\webright ) = R_{*}\webleft (U\cup V\webright ),\\ R_{*}\webleft (\text{Ø}\webright ) = \text{Ø}, \end{gathered} \]

    natural in $U,V\in \mathcal{P}\webleft (A\webright )$.


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