File:First-isomorphism-theorem.svg

2008-11-13 (first version); 2008-11-13 (last version)

Created as per: en:meta:Help:Displaying a formula#Commutative diagrams

\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package
                                % Using postscript driver for smoother curves
\usepackage{color}              % For invisible frame
\begin{document}

\newcommand{\im}{\operatorname{im}}
% \newcommand{\stack}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}
\newcommand{\stack}[2]{\underset{#2}{#1}}

\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix @=1pt@! { %We want equal spacing, and the entries close together
           &                        & 0 \ar[dr]                   &                                                          & 0\\
           &                        &                             & \stack{G / \ker f}{\cong\;\im f} \ar[ur] \ar[dr]^{\iota} & \\
           &                        & G \ar[rr]^{f} \ar[ur]^{\pi} &                                                          & H\\
           & \ker f \ar[ur]^{\kappa}&                             &                                                          & \\
  0\ar[ur] &                        &                             &                                                          &
}

$$}}} % end math, end frame
\end{document}

Michael K. Edwards