## 56.1 Introduction

Let $X$ and $Y$ be schemes. This chapter circles around the relationship between functors $\mathit{QCoh}(\mathcal{O}_ Y) \to \mathit{QCoh}(\mathcal{O}_ X)$ and morphisms of schemes $X \to Y$. More broadly speaking we study the relationship between $\mathit{QCoh}(\mathcal{O}_ X)$ and $X$ or, if $X$ is Noetherian, the relationship between $\textit{Coh}(\mathcal{O}_ X)$ and $X$. This relationship was studied in [Gabriel].

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