## Tag `03HV`

Chapter 28: Morphisms of Schemes > Section 28.24: Flat morphisms

Lemma 28.24.8. Let $f : X \to S$ be a flat morphism of schemes. Then generalizations lift along $f$, see Topology, Definition 5.19.3.

Proof.See Algebra, Section 10.40. $\square$

The code snippet corresponding to this tag is a part of the file `morphisms.tex` and is located in lines 4319–4324 (see updates for more information).

```
\begin{lemma}
\label{lemma-generalizations-lift-flat}
Let $f : X \to S$ be a flat morphism of schemes.
Then generalizations lift along $f$, see
Topology, Definition \ref{topology-definition-lift-specializations}.
\end{lemma}
\begin{proof}
See Algebra, Section \ref{algebra-section-going-up}.
\end{proof}
```

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