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aisejohan committed May 17, 2024
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Expand Up @@ -23606,6 +23606,7 @@ \section{Formal glueing of module categories}
we can find a surjection $M' \to M$ with $M'$ a direct sum of
modules of the form $R/I^n$. Using the long exact sequence of
Homology, Lemma \ref{homology-lemma-six-term-sequence-ext}
and using Lemma \ref{lemma-neighbourhood-equivalence}
we see that it suffices to prove the lemma for $M'$.
Using compatibility of $\Ext$ with direct sums (details omitted)
we reduce to the case where $M = R/I^n$ for some $n$.
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