diff --git a/inputs/lecture_15.tex b/inputs/lecture_15.tex
index 6f3f804..d77054f 100644
--- a/inputs/lecture_15.tex
+++ b/inputs/lecture_15.tex
@@ -255,7 +255,7 @@ Recall:
 \begin{definition}
     Let $\Sigma = \{(X_i, T) : i \in I\} $
     be a collection of factors of $(X,T)$. % TODO State precise definition of a factor
-    Let $\pi_i\colon (X,T) \to (X_i, T)$ denote the factor map.
+    Let $\pi_i\colon (X,T) \to (X_i, T)$ denote the factor maps.
     Then $(X, T)$ is the \vocab{limit}  of $\Sigma$
     iff
     \[
diff --git a/inputs/lecture_17.tex b/inputs/lecture_17.tex
index 8f6f36e..39cce2f 100644
--- a/inputs/lecture_17.tex
+++ b/inputs/lecture_17.tex
@@ -169,6 +169,7 @@ In particular,
 for $x \in X$ and $\overline{Tx} = Y$
 we have that $(Y,T)$ is a flow.
 However if we pick $y \in Y$, $Ty$ might not be dense.
+% TODO: question!
 % TODO: think about this!
 % We want to a minimal subflow in a nice way: