Diagrams for https://math.stackexchange.com/a/2374488/116766

Extensions.svg

Extensions.tex

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  0 \rar & \bigoplus_j D_j' \rar                      & \bigoplus_j D_j'  \rar                      & 0
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Graph1.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{amsmath}
\usepackage{tikz-cd}
\tikzcdset{arrow style=math font}
\begin{document}
\begin{tikzcd}[column sep=-2ex,row sep=large]
  & \Gamma\arrow[bend right]{ddl}[sloped,swap]{\sim}\arrow[bend left]{ddr}[sloped]{\sim}\dar[hook]\\
  & \mathscr{F}\rvert_U \oplus \mathscr{G}\rvert_U\arrow{dl}\arrow{dr}\\
  \mathscr{F}\rvert_U \arrow{rr}{\sim} & & \mathscr{G}\rvert_U
\end{tikzcd}
\end{document}

Graph2.svg

Graph2.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{amsmath}
\usepackage{tikz-cd}
\tikzcdset{arrow style=math font}
\begin{document}
\begin{tikzcd}[column sep=0,row sep=large]
  & \widetilde{\Gamma}\arrow[bend right]{ddl}[swap]{f}\arrow[bend left]{ddr}{g}\dar[hook]\\
  & \mathscr{F} \oplus \mathscr{G}\arrow{dl}\arrow{dr}\\
  \mathscr{F} & & \mathscr{G}
\end{tikzcd}
\end{document}