The Stacks project

Lemma 45.4.3. The category $M_ k$ with tensor product defined as above is symmetric monoidal with the obvious associativity and commutativity constraints and with unit $\mathbf{1} = (\mathop{\mathrm{Spec}}(k), 1, 0)$.

Proof. Follows readily from Lemma 45.3.8. Details omitted. $\square$

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