Diagrams for http://math.stackexchange.com/a/1284823/116766

HomotopyNotAbelian1.svg

HomotopyNotAbelian1.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{mathtools}
\usepackage{tikz-cd}
\tikzcdset{arrow style=math font}
\begin{document}
\[  
  \begin{tikzcd}
    C\beta[-1]
    \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\rar
    & B \arrow[-, double equal sign distance]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\rar
    & C\alpha
    \arrow[-, double equal sign distance]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\\[-0.5em]
    {} & {} & {}\\[-2.3em]
    \vdots\dar & \vdots\dar & \vdots\dar\\
    B_1 \rar{\mathrm{id}}\dar[swap]{d_1} & B_1 \rar[rightarrowtail]{\iota_2}
    \dar[swap]{d_1} & \mathbf{Z} \mathrlap{{} \oplus B_1}
    \dar{(-\alpha\ d_1)}\\
    B_0 \rar{\mathrm{id}}
    \dar[swap]{\left(\begin{smallmatrix}d_0\\\beta\end{smallmatrix}\right)}
    \arrow{ur}{h_0} & B_0 \rar{\mathrm{id}}\dar[swap]{d_0}\arrow{ur}{k_0} &
    B_0\dar{d_0}\\
    \mathllap{B_{-1} \oplus {}} \mathbf{Z}/(p) \rar[twoheadrightarrow]{p_1}
    \dar\arrow{ur}{h_{-1}} & B_{-1}
    \rar{\mathrm{id}}\dar\arrow{ur}{k_{-1}} & B_{-1} \dar\\
    \vdots & \vdots & \vdots
  \end{tikzcd}
\]
\end{document}

HomotopyNotAbelian2.svg

HomotopyNotAbelian2.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{mathtools}
\usepackage{tikz-cd}
\tikzcdset{arrow style=math font}\begin{document}
\[  
  \begin{tikzcd}
    C\beta[-1]
    \arrow[-, double equal sign distance,start anchor={[yshift=2pt]}]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\rar
    & B \arrow[-, double equal sign distance]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\rar
    & C\alpha
    \arrow[-, double equal sign distance]{d}[description,pos=0.9]{\overbrace{\hspace{3em}}}\\[-.5em]
    {} & {} & {}\\[-2.3em]
    \vdots\dar & \vdots\dar & \vdots\dar\\
    0 \rar\dar & 0 \rar
    \dar & \mathbf{Z}
    \dar\\
    B_0 \rar
    \dar
    \arrow{ur} & B_0 \rar\dar\arrow{ur}{k} &
    B_0\dar\\
    \mathbf{Z}/(p) \rar
    \dar\arrow{ur}{h} & 0
    \rar\dar\arrow{ur} & 0 \dar\\
    \vdots & \vdots & \vdots
  \end{tikzcd}
\]
\end{document}