lie-algebras-and-their-representations

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -628,8 +628,10 @@ obstructions to complete reducibility. Explicitly\dots
 This is essentially a consequence of Example~\ref{ex:hom-invariants-are-g-homs}
 and Theorem~\ref{thm:ext-1-classify-short-seqs}, as well as the minimality
 conditions that characterize \(\operatorname{Ext}^1\). For the readers already
-familiar with homological algebra: this natural isomorphism can be explicitly
-described by considering a canonical free resolution
+familiar with homological algebra: the correspondence between
+\(H^1(\mathfrak{g}, \operatorname{Hom}(L, N))\) and short exact sequences of
+\(\mathfrak{g}\)-modules can be described in very concrete terms by considering
+a canonical free resolution
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