• Interaction With Inverse Images. Let $f\colon X\to X'$ and $g\colon Y\to Y'$ be functions. The diagram

    commutes, i.e. we have

    \[ \webleft [f^{-1}\times g^{-1}\webright ]\webleft (U\boxtimes _{X'\times Y'}V\webright )=f^{-1}\webleft (U\webright )\boxtimes _{X\times Y}g^{-1}\webleft (V\webright ) \]

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


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