lie-algebras-and-their-representations

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -493,11 +493,11 @@ We are particularly interested in the case where \(L' = K\) is the trivial
   K\text{-}\mathbf{Vect}\).
 \end{definition}
 
-The Lie algebra
-cohomology groups are very much related to invariants of
+The Lie algebra cohomology groups are very much related to invariants of
 \(\mathfrak{g}\)-modules. Namely, constructing a \(\mathfrak{g}\)-homomorphism
 \(f : K \to M\) is precisely the same as fixing an invariant of \(M\) --
-corresponding to \(f(1)\). Formally, this translates to the existence of a
+corresponding to \(f(1)\), which must be an invariant for \(f\) to be a
+\(\mathfrak{g}\)-homomorphism. Formally, this translates to the existence of a
 canonical isomorphism of functors
 \(\operatorname{Hom}_{\mathfrak{g}}(K, -) \isoto {-}^{\mathfrak{g}}\) given by
 \begin{align*}