How can I draw this diagram in Latex?
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Use the tikz-cd package:
\documentclass{article}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
G & B \arrow[l,"\psi"above]\arrow[d]\arrow[r,"g"] & C \
& B/f(A) \arrow[lu,"\psi'"] \arrow[ru,"g'"below,"\simeq"above] &
\end{tikzcd}
\end{document}
Stephen
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