Whitespace cleanup.

[mjotex.git] / mjo-arrow.tex

diff --git a/mjo-arrow.tex b/mjo-arrow.tex
index 3ae2daac179659b681c3ab9d14990250cf80bb31..8b44ded1753eb175124ed71fa73ad4e5ec9b35e5 100644 (file)
--- a/mjo-arrow.tex
+++ b/mjo-arrow.tex
@@ -2,9 +2,17 @@
 % 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}} }
 
 % The composition of two arrows/functions. For example, the
 % composition of g with f is \compose{g}{f}\of{x} === g\of{f\of{x}}.
-\newcommand*{\compose}[2]{ {#1} \circ {#2} }
+\newcommand*{\compose}[2]{ {#1}\circ{#2} }
+
+% 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} }