Lemma 3.9.1. For every cardinal $\kappa$, there exists a set $A$ such that every element of $A$ is a scheme and such that for every scheme $S$ with $\text{size}(S) \leq \kappa$, there is an element $X \in A$ such that $X \cong S$ (isomorphism of schemes).

Proof. Omitted. Hint: think about how any scheme is isomorphic to a scheme obtained by glueing affines. $\square$

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