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Fix mistake in algebra.tex
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aisejohan committed Nov 4, 2014
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Showing 1 changed file with 6 additions and 5 deletions.
11 changes: 6 additions & 5 deletions algebra.tex
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Expand Up @@ -28527,11 +28527,12 @@ \section{Colimits and maps of finite presentation}
$$
S \to S_\lambda \to S
$$
for some $\lambda$. Hence we see that $S$ is finitely generated
over $R$ (because $S_\lambda$ is). Thus we may choose the system
such that all transition maps are surjective. In this case
a factorization of the identity as above can only exist if
$S = S_\lambda$.
for some $\lambda$. This impies that $S$
is finitely presented over $S_\lambda$ by
Lemma \ref{lemma-compose-finite-type} part (4)
applied to $S \to S_\lambda \to S$. Applying part (2) of the same
lemma to $R \to S_\lambda \to S$ we conclude that $S$ is of finite
presentation over $R$.
\end{proof}

\noindent
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