From 987368c596bfe23dbcbaf5260a0d7011c9d3fc1e Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 27 Oct 2016 16:52:15 -0400
Subject: [PATCH] Add the \preimage macro.

---
 examples.tex  | 3 ++-
 mjo-arrow.tex | 5 +++++
 2 files changed, 7 insertions(+), 1 deletion(-)

diff --git a/examples.tex b/examples.tex
index 98ddfd5..e0ffcb9 100644
--- a/examples.tex
+++ b/examples.tex
@@ -28,7 +28,8 @@
   \begin{section}{Arrow}
     The identity operator on $V$ is $\identity{V}$. The composition of
     $f$ and $g$ is $\compose{f}{g}$. The inverse of $f$ is
-    $\inverse{f}$.
+    $\inverse{f}$. If $f$ is a function and $A$ is a subset of its
+    domain, then the preimage under $f$ of $A$ is $\preimage{f}{A}$.
   \end{section}
 
   \begin{section}{Common}
diff --git a/mjo-arrow.tex b/mjo-arrow.tex
index 75b70c9..8b44ded 100644
--- a/mjo-arrow.tex
+++ b/mjo-arrow.tex
@@ -2,6 +2,8 @@
 % Things dealing with arrows in a category. Or functions, basically.
 %
 
+\input{mjo-common}
+
 % The identity operator/arrow on its argument.
 \newcommand*{\identity}[1]{ \operatorname{id}_{{#1}} }
 
@@ -11,3 +13,6 @@
 
 % The inverse of an arrow, function, or whatever.
 \newcommand*{\inverse}[1]{ #1^{-1} }
+
+% The preimage of the second argument (a set) under the first (a function).
+\newcommand*{\preimage}[2]{ #1^{-1}\of{#2} }
-- 
2.43.2