\begin{tikzcd}[column sep=small]
A \arrow[r] \arrow[d] & H^0(X, \mathcal{O}_X) \arrow[r, bend left=8, "p_1"] \arrow[r, bend right=8] \arrow[d] & H^0(R, \mathcal{O}_R) \arrow[d] \\
A_0 \arrow[r] & H^0(X_0, \mathcal{O}_{X_0}) \arrow[r, bend left=8, "p_2"] \arrow[r, bend right=8] & H^0(R_0, \mathcal{O}_{R_0})
\end{tikzcd}

\begin{tikzcd}
Y & X \arrow[l] & R \arrow[l, bend left=8] \arrow[l, bend right=8] \\
Y_0 \arrow[u] & X_0 \arrow[l, hook'] \arrow[u] & R_0 \arrow[l, bend left=8] \arrow[l, bend right=8] \arrow[u]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_i \arrow[d] & U_{\alpha\beta} \arrow[l] \arrow[d] \\
X & U_\alpha \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_i \arrow[d] & U_{\alpha\beta} \arrow[l] \arrow[d] \\
X & U_\alpha \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_i \arrow[d] & U_{\alpha\beta} \arrow[l] \arrow[d] & \\
X & U_\alpha \arrow[l] & \\
X'_i \arrow[uu, bend left=20] \arrow[d] & U'_{\alpha\beta} \arrow[l] \arrow[d] & U'_{\alpha\beta\lambda} \arrow[l] \arrow[d] \\
X' \arrow[uu, bend left=30] & U'_\alpha \arrow[l] \arrow[uu, bend right=20] & U'_{\alpha\lambda} \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_{ij} \arrow[d] & X_{ij} \times_{X_i} U_{\alpha\beta} \arrow[l] \arrow[d] & U_{\alpha\beta\gamma\delta} \arrow[l] \arrow[d] \\
X_i \arrow[d] & U_{\alpha\beta} \arrow[l] \arrow[d] & U_{\alpha\beta\gamma} \arrow[l] \\
X & U_\alpha \arrow[l] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
S' \arrow[d] & \\
S & S_\alpha \arrow[l] \arrow[lu, bend right=30, no head]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X \arrow[d, bend left=20] & f^{-1}(Y_i) \arrow[d, bend left=20] \\
Y \arrow[u, bend left=20, "s"] & Y_i \arrow[u, bend left=20, "s_i"]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_0^{*} \arrow[d] & X'^{*}_0 \arrow[l] \arrow[d] \\
Y & Y' \arrow[l] \\
Y^{*}_{\ill{}} \arrow[u] & Y'^{*}_{\ill{}} \arrow[l] \arrow[u]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & t' \arrow[dr, "\mathcal{U}"] & \\
t_1 \arrow[ur, "\mathcal{U}"] \arrow[r, "\mathcal{U}"] \arrow[dr, "\mathcal{U}"'] & t''' \arrow[u, "\mathcal{U}"'] \arrow[d, "\mathcal{U}"] \arrow[r, "\mathcal{U}"] & t_2 \\
 & t'' \arrow[ur, "\mathcal{U}"'] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & & t''' \arrow[ddrr, bend left=40, "\mathcal{U}"] & & \\
 & t' \arrow[ur] \arrow[dr] & & t'' \arrow[ul, no head] \arrow[dr] & \\
t_1 \arrow[uurr, bend left=40, "\mathcal{U}"] \arrow[ur] & & t_2 \arrow[ur] & & t_3
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & X \arrow[d] \\
s \in S & T \arrow[l]
\end{tikzcd}

\begin{tikzcd}
T \arrow[r, "\varphi_g"] \arrow[d, "\Delta"'] & \mathcal{U}_g \arrow[d, "\mathrm{ind.}"] \\
T \times_S T \arrow[r, "g \times e"'] & T \times_S T
\end{tikzcd}