• Interaction With Products. Let $f\colon X\to X'$ and $g\colon Y\to Y'$ be maps of sets. We have
    \[ \webleft (f\boxtimes _{X\times Y} g\webright )_{!}\webleft (U\boxtimes _{X\times Y}V\webright )=f_{!}\webleft (U\webright )\boxtimes _{X'\times Y'}g_{!}\webleft (V\webright ) \]

    for each $U\in \mathcal{P}\webleft (X\webright )$ and each $V\in \mathcal{P}\webleft (Y\webright )$.


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