diff --git a/symmetric_tensor_categories_fiber_v2.txt b/symmetric_tensor_categories_fiber_v2.txt
index 6968920..96baa42 100644
--- a/symmetric_tensor_categories_fiber_v2.txt
+++ b/symmetric_tensor_categories_fiber_v2.txt
@@ -1182,6 +1182,51 @@ vertices belong to $\mathcal C_{\mathrm{ex}}$, and each vertex has
 exactly one outgoing arrow.  Hence a path entering a cycle is
 trapped inside it.  A path of length $N$ visits $N+1$ vertices and
 so hits a cycle.  Its endpoint is in $\mathcal C_{\mathrm{ex}}$.
+A schematic path is drawn in \cref{fig:dimension-descent}.
+
+\begin{figure}[!htbp]
+\centering
+\begin{tikzpicture}[
+  x=1cm,y=1cm,
+  vertex/.style={circle,draw,fill=white,minimum size=5mm,inner sep=0pt},
+  edge/.style={-{Stealth[length=2mm]},semithick},
+  every node/.style={font=\small}
+]
+  \fill[black!4,rounded corners=5pt] (0.1,-1.65) rectangle (3.55,1.8);
+  \node at (-2.8,1.45) {nonincreasing dimension};
+  \node at (1.83,2.10) {equal dimension};
+  \node[vertex] (S0) at (-4.4,0) {};
+  \node[vertex] (S1) at (-2.8,0) {};
+  \node[vertex] (S2) at (-1.2,0) {};
+  \node[vertex] (A) at (0.7,0) {};
+  \node[vertex] (B) at (2.7,1) {};
+  \node[vertex] (C) at (2.7,-1) {};
+  \node[above=5pt] at (S0.north) {$S_0$};
+  \node[above=5pt] at (S1.north) {$S_1$};
+  \node[above=5pt] at (S2.north) {$S_2$};
+  \node[above left=5pt] at (A.north west) {$A$};
+  \node[above=5pt] at (B.north) {$B$};
+  \node[right=5pt] at (C.east) {$C$};
+  \draw[edge] (S0) -- (S1);
+  \draw[edge] (S1) -- (S2);
+  \draw[edge] (S2) -- (A);
+  \draw[edge] (A) -- (B);
+  \draw[edge] (B) -- (C);
+  \draw[edge] (C) -- (A);
+  \node[align=center] at (-2.8,-0.95)
+    {$S\longrightarrow S'$ implies $d(S')\leq d(S)$};
+  \node[align=center] at (1.83,-2.10)
+    {$A,B,C\in\mathcal C_{\mathrm{ex}}$\\[2pt]
+     unique outgoing neighbor at each cycle vertex};
+\end{tikzpicture}
+\caption{A schematic path in the graph of simple objects, with an
+illustrative three-vertex cycle.  Dimension is nonincreasing along
+every arrow; arrows before the cycle may also preserve dimension.
+On a cycle, \cref{lem:first-component-inequality} gives equality,
+membership in $\mathcal C_{\mathrm{ex}}$, and a unique outgoing
+neighbor at every vertex, so the path cannot leave the cycle.}
+\label{fig:dimension-descent}
+\end{figure}
 
 \subsection{Iteration and Serre closure}