ScalingStacks

Proposition 25 The complex $\overline{C}(D)$ is quasiisomorphic to the total complex ${\mathrm{Tot}}(C^{\prime})$ of the bicomplex $C^{\prime}.$ Cohomology groups $\overline{H}^{i}(D)$ are isomorphic to the cohomology groups of ${\mathrm{Tot}}(C^{\prime}).$