# HG changeset patch
# User Benedikt Fluhr <http://bfluhr.com>
# Date 1445696033 -7200
#      Sat Oct 24 16:13:53 2015 +0200
# Node ID 2974fa163cd17312596a9027d8490f7cf29d826b
# Parent  f832c5223a7dfc0ff3b027a3144b03e615cd916a
Added remark about surjectivity of hom(_, A)

diff --git a/06_fromSetsToAlgebras.md b/06_fromSetsToAlgebras.md
--- a/06_fromSetsToAlgebras.md
+++ b/06_fromSetsToAlgebras.md
@@ -98,6 +98,17 @@
 $1_{m(1)} \in \mathfrak{a} \subset \mathfrak{m}$ is mapped to
 $1 \in \Z / p \Z$ under $\hom(m, \Z / p \Z)$.
 
+* *Remark.*
+From a discussion similar to that of the previous lemma and example
+we can conclude that for sets $K$ and $L$ with $L$ non-empty, the map
+from $\hom(L, K)$ to
+$\hom_{A\text{-algebras}} (\hom(K, A), \hom(L, A))$
+induced by $\hom(\_, A)$ is surjective if and only if all
+ideals^[which are prime necessarily] $\mathfrak{p}$ of $\hom(K, A)$,
+with $\hom(K, A) / \mathfrak{p} \cong A$ as $A$-algebras,
+are of the form
+$\set{c}{\hom(K, A)}{c(k) = 0}$ for some $k \in K$.
+
 * **Lemma.**
 $\hom(\_, A)$ is continuous as a functor from the opposed category of sets
 to the category of $A$-algebras.