Author: nLab edit announcer Format: MarkdownItexThe individual morphisms $f_i$ are not usually *faithfully* flat -- any faithfully flat morphism is surjective. I think they are also not quasicompact in general. See the definition of fpqc cover in the stacks project:
https://stacks.math.columbia.edu/tag/01K2
Anonymous
<a href="https://ncatlab.org/nlab/revision/diff/fpqc+topology/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/fpqc+topology/8">v8</a>, <a href="https://ncatlab.org/nlab/show/fpqc+topology">current</a>
The individual morphisms $f_i$ are not usually faithfully flat – any faithfully flat morphism is surjective. I think they are also not quasicompact in general. See the definition of fpqc cover in the stacks project: