• given $X$ in $\mathcal{C}$ and $\mathcal{F}'$ in $\mathcal{A}'_ X$, then $\mathcal{F}'$ satisfies the sheaf condition for $\tau$-coverings, i.e., $\mathcal{F}' = \epsilon _{X, *}\epsilon _ X^{-1}\mathcal{F}'$,

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