ScalingStacks

Proposition 4 Let $V$ be a skew $\mathcal{I}$-cube over an abelian category $\mathcal{B}$ and suppose that for some $a\in\mathcal{I}$ and any $\mathcal{L}\subset\mathcal{I}\setminus\{a\}$ the map $\xi^{V}_{a}:V(\mathcal{L})\to V(\mathcal{L}a)$ is an isomorphism. Then the complex $\overline{C}(V)$ is acyclic.