Fix example

Argh... not sure what I was thinking before...

sites.tex

@@ -4950,17 +4950,19 @@ \section{Cocontinuous functors which have a right adjoint}
 Lemma \ref{lemma-continuous-with-continuous-left-adjoint}
 shows that if $v$ is continuous, then $u$ is cocontinous.
 Conversely, if $u$ is cocontinuous, then we can't conclude that $v$
-is continuous. Namely, consider a topological space $X$ and
-the site $X_{Zar}$ of Example \ref{example-site-topological}.
-On the other hand, given an open covering $X = W \cup V$
-we can consider the site $X'_{Zar}$ defined in exactly the
-same manner, except that we declare $U = \bigcup U_i$ to be
-a covering if and only if for each $i$ either $U_i \subset W$
-or $U_i \subset V$. Set $u = v = \text{id}$. Then
-$v$ viewed as functor $X'_{Zar} \to X_{Zar}$ is continuous
-(as any covering in $X_{Zar}$ can be refined by a covering in
-$X'_{Zar}$) but $u$ viewed as a functor $X_{Zar} \to X'_{Zar}$
-is not continuous (provided neither $W \not = X$ and $V \not = X$).
+is continuous. We will give an example of this phenomenon using
+the big \'etale and smooth sites of a scheme, but presumably there is an
+elementary example as well. Namely, consider a scheme $S$ and the sites
+$(\Sch/S)_\etale$ and $(\Sch/S)_{smooth}$. We may assume these
+sites have the same underlying category, see
+Topologies, Remark \ref{topologies-remark-choice-sites}.
+Let $u = v = \text{id}$. Then $u$ as a functor
+from $(\Sch/S)_\etale$ to $(\Sch/S)_{smooth}$ is cocontinuous
+as every smooth covering of a scheme can be refined by an \'etale
+covering, see More on Morphisms, Lemma
+\ref{more-morphisms-lemma-etale-dominates-smooth}.
+Conversely, the functor $v$ from $(\Sch/S)_{smooth}$ to $(\Sch/S)_\etale$
+is not continuous as a smooth covering is not an \'etale covering in general.
 \end{example}