lie-algebras-and-their-representations

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -134,6 +134,9 @@ discuss some further reductions to our general problem, the first of which is a
 crutial refinement to Proposition~\ref{thm:coherent-families-are-all-ext} due
 to Mathieu.
 
+% TODO: Note that we may take L(λ) with respect to any given basis
+% TODO: Note beforehand that the construction of Verma modules and the notions
+% of highest-weight modules in gerenal is relative on a choice of basis
 \begin{proposition}\label{coh-family-is-ext-l-lambda}
   Let \(\mathcal{M}\) be a semisimple irreducible coherent
   \(\mathfrak{g}\)-family. Then there exists some \(\lambda \in
@@ -144,7 +147,7 @@ to Mathieu.
 \begin{note}
   I once had the opportunity to ask Olivier Mathieu himself how he first came
   across the notation of coherent families and what was his intuition behind
-  it. Unfortunately, his responce was that ``he did not remember.'' However,
+  it. Unfortunately, his responce was that he ``did not remember.'' However,
   Mathieu was able to tell me that ``the \emph{trick} is that I managed to show
   that they all come from simple highest-weight modules, which were already
   well understood.'' I personally find it likely that Mathieu first considered