Definition 21.41.1. Let $\mathcal{C}$ be a site. Let $\mathcal{A}_\bullet $ be a simplicial sheaf of rings on $\mathcal{C}$. A simplicial $\mathcal{A}_\bullet $-module $\mathcal{F}_\bullet $ (sometimes called a simplicial sheaf of $\mathcal{A}_\bullet $-modules) is a sheaf of modules over the sheaf of rings on $\Delta \times \mathcal{C}$ associated to $\mathcal{A}_\bullet $.
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