The Stacks project

Remark 94.8.3. Note that the whole discussion in this section works if we want to consider those algebraic spaces $X/U$ which are locally of finite type such that the inverse image in $X$ of an affine open of $U$ can be covered by countably many affines. If needed we can also introduce the notion of a morphism of $\kappa $-type (meaning some bound on the number of generators of ring extensions and some bound on the cardinality of the affines over a given affine in the base) where $\kappa $ is a cardinal, and then we can produce a stack

\[ \mathcal{S}\! \mathit{paces}_\kappa \longrightarrow (\mathit{Sch}/S)_{fppf} \]

in exactly the same manner as above (provided we make sure that $\mathit{Sch}$ is large enough depending on $\kappa $).


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