lie-algebras-and-their-representations

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -789,6 +789,16 @@ then follows\dots
   finite-dimensional repesentations to finitely generated modules.
 \end{proposition}
 
+\begin{note}
+  We should point out that the monoidal structure of
+  \(\mathfrak{g}\text{-}\mathbf{Mod}\) is \emph{not} the same as that of
+  \(\mathcal{U}(\mathfrak{g})\text{-}\mathbf{Mod}\). In other words, \(V
+  \otimes W\) is not the same thing as \(V \otimes_{\mathcal{U}(\mathfrak{g})}
+  W\) and hence the equivalence \(\mathfrak{g}\text{-}\mathbf{Mod} \isoto
+  \mathcal{U}(\mathfrak{g})\text{-}\mathbf{Mod}\) does not preserve tensor
+  products.
+\end{note}
+
 Representations are the subjects of \emph{representation theory}, a field
 dedicated to understanding a Lie algebra \(\mathfrak{g}\) via its
 \(\mathfrak{g}\)-modules. The fundamental problem of representation theory is a