ScalingStacks

Definition 2.67. Let $\mathfrak{V}$ be an admissible covering of $\mathfrak{M}(\mathcal{A})$ by affinoid domains $\{V_{i}\}_{i\in I}$, where $I$ is a finite set. Then for a Banach finite $\mathcal{A}$-module $\mathcal{M}$, the Cech complex of $\mathcal{M}$ with respect to $V_{i}$ is defined to be the complex of Banach $\mathcal{A}$-modules

$$C^{\centerdot}(\mathcal{M},\mathfrak{V}):\text{ }0\to\mathcal{M}\to\prod_{i\in I}\mathcal{M}_{i}\to\prod_{i,j\in I}\mathcal{M}_{i,j}\to\dots$$