diff --git a/III_M/algebraic_topology_iii.tex b/III_M/algebraic_topology_iii.tex
index 3320153..055b176 100644
--- a/III_M/algebraic_topology_iii.tex
+++ b/III_M/algebraic_topology_iii.tex
@@ -2456,7 +2456,7 @@ \section{Cup product}
 \end{prop}
 
 \begin{proof}[Proof of previous proposition]
-  Let $\rho_n: C_n(X) \to C_n(x)$ be given by
+  Let $\rho_n: C_n(X) \to C_n(X)$ be given by
   \[
     \sigma \mapsto (-1)^{n(n + 1)/2} \sigma|_{[v_n, v_{n - 1}, \ldots, v_0]}
   \]