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The Stacks project

Definition 92.18.1. Let \mathcal{C} be a site. Let \mathcal{A} \to \mathcal{B} be a homomorphism of sheaves of rings on \mathcal{C}. The standard resolution of \mathcal{B} over \mathcal{A} is the augmentation \epsilon : \mathcal{P}_\bullet \to \mathcal{B} with terms

\mathcal{P}_0 = \mathcal{A}[\mathcal{B}],\quad \mathcal{P}_1 = \mathcal{A}[\mathcal{A}[\mathcal{B}]],\quad \ldots

and maps as constructed above.


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