From: Michael Orlitzky Date: Thu, 27 Oct 2016 20:52:15 +0000 (-0400) Subject: Add the \preimage macro. X-Git-Tag: phd-dissertation-submitted~22 X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=987368c596bfe23dbcbaf5260a0d7011c9d3fc1e;p=mjotex.git Add the \preimage macro. --- 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} }