\begin{tikzcd}
C \arrow[r, "\varphi"] & C' \arrow[r, "\nu"] & D' \\
A & A' &
\end{tikzcd}

\begin{tikzcd}[column sep=small]
  \det(M) \arrow[rr, "c"] \arrow[dr, no head, "u_{\xi}(M{,}o)"'] & &
  \det M' \arrow[dl, no head, "u_{\xi}(M'{,}o')"] \\
  & T_{p} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=large, nodes={font=\small}]
 & \mathrm{Eqv}(C,C) \arrow[dl, "\alpha_{X}"'] \arrow[dr] & \\
 (o,o)\text{-bimodules spéciaux} \arrow[rr, "L \mapsto PLP^{-1}"] & & (o',o')\text{-bimodules spéciaux}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
  \mathbf{Q}'(i) \arrow[r, no head] \arrow[d, no head] & L \arrow[d, no head] \arrow[dr, no head] & \\
  \mathbf{Q}' \arrow[r, no head] & K \arrow[dd, no head] \arrow[dr, no head] & L_{0} \arrow[d, no head] \\
  & & K_{0} \\
  & \mathbf{Q} &
\end{tikzcd}

\begin{tikzcd}
  \mathbf{G}_{m\,L_{0}} \arrow[r, "v'"] \arrow[d, no head, "\Vert" description] & G'_{L_{0}} \arrow[d] \\
  \mathbf{G}_{m\,L_{0}} \arrow[r, "v"] & G_{L_{0}}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathbb{K} \arrow[r, no head] \arrow[d, no head] & \mathbb{K}(L) \arrow[r, no head] \arrow[d, no head] & \mathbb{L} \\
K = \mathbb{K} \cap L \arrow[r, no head] \arrow[d, no head] & L & \\
\mathbb{Q} & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathcal{M}_{0} \arrow[r, no head] & \mathcal{M}^{(0)} \\
 & \mathcal{M}' \arrow[u]
\end{tikzcd}

\begin{tikzcd}
\mathcal{G}_{\varphi} \arrow[r] & \mathcal{G} \\
\mathcal{G}_{\chi} \arrow[u] \arrow[r] & \mathcal{G}_{\psi} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
 & G' & \\
V \arrow[r] & G \arrow[u] \arrow[r, "\varepsilon"] & \mathbb{G}_{m} \\
U \arrow[u] \arrow[r] & G^{0} \arrow[u] &
\end{tikzcd}

\begin{tikzcd}
G' \arrow[r, hook] \arrow[d] & G \arrow[d] \\
\Gamma' \arrow[r, no head] & \Gamma
\end{tikzcd}

\begin{tikzcd}
\mathcal{G}'_{\varphi'} \arrow[r, no head] & \mathcal{G}' \\
\mathcal{G}'_{\chi'} \arrow[u] \arrow[r] & \mathcal{G}'_{\psi'} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
\mathcal{G}_{\varphi} \arrow[r, no head] & \mathcal{G} \\
\mathcal{G}_{\chi} \arrow[u] \arrow[r, no head] & \mathcal{G}_{\psi} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
V' \arrow[r] & G' \\
U' \arrow[u] \arrow[r] & G'^{0} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
V \arrow[r, no head] & G \\
U \arrow[u] \arrow[r, no head] & G^{0} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
\mathbb{Z} \arrow[r, hook] & N \arrow[r, hook] & \mathbb{Z}[I_{K}] \\
\mathbb{Z} \arrow[u, "\wr" description, no head] \arrow[rr, hook] & & \mathbb{Z}[I_{L}] \arrow[u, hook]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
K \arrow[r, no head, "Q"] \arrow[d, no head, "H"'] & \widetilde{K} \arrow[d, no head, "P"] \\
L = K \cap K' \arrow[r, no head] \arrow[d, no head] & K' \\
\mathbb{Q} \arrow[ur, no head, "G' = G/P"'] \arrow[uur, no head, bend right=40, "G"'] &
\end{tikzcd}

\begin{tikzcd}
1 \arrow[r] & V_{K} \arrow[r] \arrow[d, "\mathrm{can}"] & T_{K} \arrow[r, "N_{K}"] \arrow[d, "\mathrm{can}"] & \mathbb{G}_{m} \arrow[r] \arrow[d, no head] & 1 \\
1 \arrow[r] & V'_{K} \arrow[r] & S^{\circ}_{K} \arrow[r] & \mathbb{G}_{m} \arrow[r] & 1
\end{tikzcd}

\begin{tikzcd}
1 \arrow[r] & V'_{K} \arrow[r] \arrow[d] & S^{\circ}_{K} \arrow[r] \arrow[d, "i_{K/K'}"] & \mathbb{G}_{m} \arrow[r] \arrow[d, "\lambda \mapsto \lambda^{r}"] & 1 \\
1 \arrow[r] & V'_{K'} \arrow[r] & S^{\circ}_{K'} \arrow[r] & \mathbb{G}_{m} \arrow[r] & 1
\end{tikzcd}

\begin{tikzcd}
T_{K'} \arrow[r, "N_{K'/K}"] \arrow[rrr, bend right=25, "\Psi_{\Sigma'}"'] & T_{K} \arrow[r, "\Psi_{\Sigma}"] & T_{E} \arrow[r, "i_{E'/E}"] & T_{E'}
\end{tikzcd}

\begin{tikzcd}[column sep=small]
0 \arrow[r] & H^{1}(\mathbb{Q}, T)' \arrow[r] & \hat{H}_{0}(\gamma, Y'_{\infty}) \arrow[r] \arrow[d, "\simeq"] & \hat{H}_{0}(\gamma, \mathbb{Z}') \arrow[r] \arrow[d, no head] & 0 \\
 & & Y_{\infty} \otimes \mathbb{Z}/2\mathbb{Z} \arrow[r, two heads] & \mathbb{Z}/2\mathbb{Z} &
\end{tikzcd}

\begin{tikzcd}
0 \arrow[r] & G^{\circ} \arrow[r] & G \arrow[r] & \gamma \arrow[r] \arrow[d, no head] & 0 \\
 & & & \mathrm{Pic}(A)^{\mathrm{abs}} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
M_{\circ} \arrow[r, "\tilde{\xi}"] \arrow[rr, bend right=20, "\text{fibre en } \xi"'] & \text{Vectoriels sur } \mathbb{Q} \text{ avec opération de } G & \text{réseaux de Hodge}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\overline{\mathcal{M}}_{0} \arrow[rr, "\text{fibre en } \tilde{\xi}"] \arrow[rr, bend right=25, "\text{fibre en } \xi'"'] & & G^{0}\text{-Modules} \arrow[rr, "\Phi_{\tilde{\xi}}"] \arrow[rr, bend right=25, no head, "\varphi"'] & & \text{Réseaux de Hodge}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
K_{\xi_{1}} & K_{\xi_{2}} & K_{\xi_{3}} \\
 & K \arrow[ul, no head] \arrow[u, no head] \arrow[ur, no head] & \\
 & \mathbb{Q} \arrow[u, no head] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & X \arrow[dd, no head] \\
\mathbb{C} \arrow[ur, no head] \arrow[dr, no head] & \\
 & \mathbb{R}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & X_0 \arrow[r, no head] \arrow[d, no head] & X \arrow[d, no head] \\
k_0 \arrow[r, no head] & A_0 \arrow[r, no head] & k
\end{tikzcd}