\begin{tikzcd}[column sep=small]
0 & I \arrow[l] & \varprojlim_g gI \arrow[l, "\alpha^{0*}"'] & D(H^2_x(F)) \arrow[l, "\partial^{*}"'] & A \arrow[l, "\alpha^{1*}"'] \arrow[dl, dashed] & 0 \arrow[l] \\
 & & & A_f \arrow[u, "\varphi"] \arrow[ul, dashed, "d"] & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
{[(\mathrm{vii}) \Leftrightarrow (\mathrm{v}) \Leftrightarrow (\mathrm{v\ bis}) \Leftrightarrow (\mathrm{v\ ter})]} \arrow[d, Rightarrow] & {[(\mathrm{iv\ bis}) \Leftrightarrow (\mathrm{iv})]} \arrow[l, Rightarrow] \arrow[d, Rightarrow] \\
(\mathrm{iii}) & (\mathrm{i\ bis}) \quad (\mathrm{i}) \quad (\mathrm{vi})
\end{tikzcd}