= Power objects in a slice category
{title2=$P_{\mathcal E/A}(A\times X)=A\times PX$}
If a <Cartesian category> has <power objects>, its <slice categories> do too. In $\mathcal E/A$, the constant family $A\times X\to A$ has power object $A\times PX\to A$, since its product with a family $Y\to A$ is $X\times Y$. An arbitrary family $p:X\to A$ is a subobject of the constant family through its graph $(p,1_X)$, so the <power object of a subobject> construction applies in the slice.
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