Remark 92.3.3. Let A \to B be a ring map. Let \mathcal{A} be the category of arrows \psi : C \to B of A-algebras and let \mathcal{S} be the category of maps E \to B where E is a set. There are adjoint functors V : \mathcal{A} \to \mathcal{S} (the forgetful functor) and U : \mathcal{S} \to \mathcal{A} which sends E \to B to A[E] \to B. Let X_\bullet be the simplicial object of \text{Fun}(\mathcal{A}, \mathcal{A}) constructed in Simplicial, Section 14.34. The diagram
commutes. It follows that X_\bullet (\text{id}_ B : B \to B) is equal to the standard resolution of B over A.
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