# Why is $Mor_S(Spec R,SpecSym_{\mathcal{O}_S}\mathcal{Q})\cong Hom_{\mathcal{O}_S-\operatorname{mod}}(\mathcal{Q},f_{*}\mathcal{O}_{R})$?

Assume $$S$$ is a Noetherian scheme and $$f:\operatorname{Spec}(R)\longrightarrow S$$ is any morphism from an affine scheme to $$S$$. Assume $$\mathcal{Q}$$ is a coherent sheaf over $$S$$ and $$\operatorname{Sym}_{\mathcal{O}_{S}}\mathcal{Q}:=\operatorname{Tens}_{\mathcal{O}_{S}}\mathcal{Q}/(a\otimes b-b\otimes a)$$ is its associated symmetrical algebra. Nitsure (https://arxiv.org/abs/math/0504590, p.17) makes the claim that $$\begin{equation*} \operatorname{Mor}_{S}(\operatorname{Spec}(R),\operatorname{Spec}\operatorname{Sym}_{\mathcal{O}_{S}}\mathcal{Q})\cong\operatorname{Hom}_{\mathcal{O}_{S}-\operatorname{mod}}(\mathcal{Q},f_{*}\mathcal{O}_{R})\text{.} \end{equation*}$$ Why is that the case?

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