Lemma 90.4.6. If $B$ is a polynomial algebra over the ring $A$, then with $\pi $ as in (90.4.0.1) we have that $\pi _!$ is exact and $\pi _!\mathcal{F} = \mathcal{F}(B \to B)$.

**Proof.**
This follows from Lemma 90.4.1 which tells us the constant simplicial algebra on $B$ can be used to compute $L\pi _!$.
$\square$

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