1 files changed, 4 insertions, 1 deletions

diff --git a/provider/posts/simmons-intro-to-cat-t/1.2.md b/provider/posts/simmons-intro-to-cat-t/1.2.md
index c714f81..e180c6d 100644
--- a/provider/posts/simmons-intro-to-cat-t/1.2.md
+++ b/provider/posts/simmons-intro-to-cat-t/1.2.md
@@ -136,6 +136,7 @@ A \arrow[r, "f"] & B \arrow[r, "g"] & C \\
 \bar{\bar{A}} \arrow[u, hook] \arrow[ru, "\rest{f}{\bar{\bar{A}}}" description] & & \\
 \end{tikzcd}
 $$
+where all restricted versions of $f$, $g$, and $h$ are total.
 
 Extending the above to three partial functions $f : A \to B$, $g : B \to C$, and $h : C \to D$:
 $$
@@ -160,7 +161,7 @@ $$
 \begin{aligned}
 \Phi : \ca{Pfn} & \to \ca{Set_\bot} \\
 A & \mapsto A \cup \{ \bot_A \} \\
-\begin{tikzcd}
+f\ \text{s.t.} \begin{tikzcd}
 A \arrow[r, "f"] & B \\
 \bar{A} \arrow[u, hook] \arrow[ru, "\rest{f}{\bar{A}}" description] & 
 \end{tikzcd} & \mapsto \begin{aligned}
@@ -176,5 +177,7 @@ A & \mapsto A - \{ \bot \} \\
 f & \mapsto \rest{f}{\left ( A - \{ \bot \} \right )}
 \end{aligned}
 $$
+where $\rest{f}{\bar{A}}$ is total.
 </div>
 </div>
+