ScalingStacks

Proposition 5 Let $V$ be an $\mathcal{I}$-cube over $R{\mbox{-mod}_{0}}$ and suppose that for some $a\in\mathcal{I}$ the structure map

$$\xi^{V}_{a}:V_{a}(\ast 0)\longrightarrow V_{a}(\ast 1)$$

(37)

is an isomorphism. Then the complex $\overline{C}(V\otimes E_{\mathcal{I}})$ is acyclic.