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

Extensions.svg

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Extensions.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{amsmath}
\usepackage{tikz-cd}
\tikzcdset{arrow style=math font}
\begin{document}
\begin{tikzcd}[row sep=small]
  0 \rar & C' \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}
                            \rar                      & C_1 \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}
                                                                          \rar                      & C''
    \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}\rar                      & 0\\[0.625em]
  0 \rar & \bigoplus_i D_i' \rar\dar[phantom]{\oplus} & \bigoplus_i D_i'  \rar\dar[phantom]{\oplus} & 0                     \dar[phantom]{\oplus}\\
         & 0                \rar\dar[phantom]{\oplus} & \bigoplus_i D_i'' \rar\dar[phantom]{\oplus} & \bigoplus_i D_i'' \rar\dar[phantom]{\oplus} & 0\\
  0 \rar & \bigoplus_j D_j' \rar                      & \bigoplus_j D_j   \rar                      & \bigoplus_j D_j'' \rar                      & 0\\[0.5em]
  0 \rar & C' \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}
                            \rar                      & C_2 \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}
                                                                          \rar                      & C''
    \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.75]{\overbrace{\hspace{3em}}}\rar                      & 0\\[0.625em]
  0 \rar & \bigoplus_i D_i' \rar\dar[phantom]{\oplus} & \bigoplus_i D_i   \rar\dar[phantom]{\oplus} & \bigoplus_i D_i'' \rar\dar[phantom]{\oplus} & 0\\
         & 0                \rar\dar[phantom]{\oplus} & \bigoplus_i D_j'' \rar\dar[phantom]{\oplus} & \bigoplus_i D_j'' \rar\dar[phantom]{\oplus} & 0\\
  0 \rar & \bigoplus_j D_j' \rar                      & \bigoplus_j D_j'  \rar                      & 0
\end{tikzcd}
\end{document}

Graph1.svg

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}