lie-algebras-and-their-representations

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -844,7 +844,9 @@ representations.
     \end{tikzcd}
   \end{center}
   commutes for all \(X \in \mathfrak{g}\). We denote the space of all
-  intertwiners \(V \to W\) by \(\operatorname{Hom}_{\mathfrak{g}}(V, W)\).
+  intertwiners \(V \to W\) by \(\operatorname{Hom}_{\mathfrak{g}}(V, W)\) -- as
+  opposed the the space \(\operatorname{Hom}(V, W)\) of all \(K\)-linear maps
+  \(V \to W\).
 \end{definition}
 
 The collection of representations of a fixed Lie algebra \(\mathfrak{g}\) thus
@@ -923,8 +925,9 @@ define\dots
 
 \begin{example}
   Given a Lie algebra \(\mathfrak{g}\) and representations \(V\) and \(W\) of
-  \(\mathfrak{g}\), the spaces \(V \wedge W\) and \(V \odot W\) are both
-  representations of \(\mathfrak{g}\): they are quotients of \(V \otimes W\).
+  \(\mathfrak{g}\), the exterior and symmetric products \(V \wedge W\) and \(V
+  \odot W\) are both representations of \(\mathfrak{g}\): they are quotients of
+  \(V \otimes W\).
 \end{example}
 
 \begin{example}