\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & & X_{\mathrm{zar}} \arrow[dll] \arrow[drr] & & \\
X_{\mathrm{conn}} \arrow[rrrr, dashed] \arrow[drr, "\text{équiv. en car. } 0"] \arrow[dd, "\text{équiv. si } X/S \text{ lisse}"'] & & & & X_{\mathbb{P}\mathrm{-conn}} \arrow[dll, dashed] \arrow[dd, "\text{équiv. si } X/p \text{ lisse}"] \\
 & & X_{\mathrm{strat}} \arrow[dd] & & \\
X_{\mathrm{cris}} \arrow[rrrr, dashed] \arrow[drr] \arrow[ddrr] & & & & X_{\mathbb{P}\mathrm{-cris}} \arrow[dll, dashed] \arrow[ddll] \\
 & & X_{\mathrm{inf}} \arrow[d] & & \\
 & & X_{\mathrm{zar}} & &
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, "F_X"] \arrow[d, "g"'] & X \arrow[d, "g"] \\
Y \arrow[r, "F_Y"] & Y
\end{tikzcd}

\begin{tikzcd}
X' \arrow[r, "\alpha"] \arrow[d, "u_1"'] & X \arrow[d, "u_0"] \\
Y' \arrow[r, "\lambda"] & Y
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, "\omega_X"] \arrow[d, "u_0"'] & \mathcal{Q}(\alpha, \beta) \arrow[d, "\mathcal{Q}(u) = v"] \\
Y \arrow[r, "\omega_Y"] & \mathcal{Q}(\lambda, \mu)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
U' \arrow[r] & U \arrow[r, hook] & X \arrow[d, "f"] \\
& & S
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\widetilde{\mathrm{Zar}}(X) \arrow[r, dashed] & \widetilde{\mathrm{DR}}_{\mathrm{st}}(X) \arrow[r] \arrow[d] & \widetilde{\mathrm{Strat}}(X) \arrow[d] \\
& \widetilde{\mathrm{DR}}(X) \arrow[r] & \widetilde{\mathrm{Cris}}(X)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\Omega^1_{B/A} \otimes_B C \arrow[r, "v"] \arrow[d, "r^{\prime} \otimes 1"'] & \Omega^1_{C/A} \arrow[r, "u"] \arrow[d, "r"'] & \Omega^1_{C/B} \arrow[r] \arrow[d, "r^{\prime\prime}"'] & 0 \\
\overline{\Omega}^1_{B/A} \otimes_B C \arrow[r, "\bar v"'] & \overline{\Omega}^1_{C/A} \arrow[r, "\bar u"'] & \overline{\Omega}^1_{C/B} \arrow[r] & 0
\end{tikzcd}