Universal flattenings are surjective

Thanks to Torsten Wedhorn
https://stacks.math.columbia.edu/tag/052F#comment-7447

flat.tex

@@ -6414,10 +6414,10 @@ \section{Flattening stratifications}
 the {\it platificateur universel}. Existence of the universal flattening
 should not be confused with the type of results discussed in
 More on Algebra, Section \ref{more-algebra-section-blowup-flat}.} of
-$\mathcal{F}$ exists, then the morphism $S' \to S$ is a monomorphism of schemes
-such that $\mathcal{F}_{S'}$ is flat over $S'$ and such that a
-morphism $T \to S$ factors through $S'$ if and only if $\mathcal{F}_T$
-is flat over $T$.
+$\mathcal{F}$ exists, then the morphism $S' \to S$ is a surjective
+monomorphism of schemes such that $\mathcal{F}_{S'}$ is flat over $S'$
+and such that a morphism $T \to S$ factors through $S'$ if and only if
+$\mathcal{F}_T$ is flat over $T$.
 
 \begin{example}
 \label{example-no-universal-flattening}