How to make a composition of functions prettier?
A solution based on alignat*
and \xmapsto
. Requires mathtools
and eqparbox
:
\documentclass[11pt]{article}
\usepackage{mathtools}
\DeclareMathOperator{\id}{id}
\usepackage{eqparbox}
\newcommand{\eqmathbox}[2][M]{\eqmakebox[#1]{$\displaystyle#2$}}
\begin{document}
\begin{alignat*}{2}
G\times U & \xrightarrow{\id\times \sigma} \eqmathbox{G\times \pi^{-1}(U)} & & \xrightarrow[\phantom{\id\times \sigma}]{\theta} \pi^{-1}(U) \\[-1.5ex]
(g, [x]) & \xmapsto{\phantom{\id\times \sigma}} \eqmathbox{(g,\sigma[x])} & & \xmapsto[\phantom{\id\times \sigma}]{} g\cdot \sigma[x]
\end{alignat*}
\end{document}
One way to align (actually, center) everything is to use some package for commutative diagrams, for example tikz-cd
:
\documentclass[11pt]{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[row sep=0pt]
G\times U \arrow[r,"\mathrm{id}\times \sigma"] & G\times \pi^{-1}(U)
\arrow[r,"\theta"] &\pi^{-1}(U) \\
(g, [x]) \arrow[r,mapsto] &(g,\sigma[x]) \arrow[r,mapsto] & g\cdot \sigma[x]
\end{tikzcd}
\]
\end{document}
(Changes after the comments: \textrm{}
is replaced by \mathrm{}
as per egreg's suggestion, the diagram is places inside display math.)
The result is:
I suppose that this will do what you want:
\documentclass[11pt]{article}
\usepackage{amsmath}
\begin{document}
\[\begin{array}{ccccc}
G\times U & \xrightarrow{\textrm{id}\times \sigma}& G\times \pi^{-1}(U) &\xrightarrow{\theta}&\pi^{-1}(U) \\
(g, [x]) &\longmapsto &(g,\sigma[x]) &\longmapsto&g\cdot \sigma[x]
\end{array}\]
\end{document}
Here is how it looks: