lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -203,6 +203,8 @@
   \(\mathfrak{sl}_2(K)\).
 \end{example}
 
+% TODOO: Do we need this proposition? I think this only comes up in the
+% classification of simple completely reducible coherent families
 \begin{proposition}
   If \(\mathfrak{g} = \mathfrak{z} \oplus \mathfrak{s}_1 \oplus \cdots \oplus
   \mathfrak{s}_n\), where \(\mathfrak{z}\) is the center of \(\mathfrak{g}\)
@@ -239,8 +241,8 @@
 % comes from the relationship between highest weight modules and coherent
 % families
 
-% TODOO: I think this is equivalent to M being a simple object in the
-% category of coherent families. This is perhaps a more intuitive formulation
+% TODO: Point out this is equivalent to M being a simple object in the
+% category of coherent families
 \begin{definition}
   A coherent family \(\mathcal{M}\) is called \emph{irreducible} if
   \(\mathcal{M}_\lambda\) is a simple