\begin{tikzcd}[column sep=small, row sep=small]
U_y \ni x_1 \arrow[d] & \\
X_y \ni x & x' \arrow[ul] \arrow[l] \\
y & y' \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
x_1 \arrow[d] & x' \arrow[l] \arrow[dl] & \hat{x}_1 & \hat{x}' \in \mathrm{Ass}\, \widehat{U} \\
x & & & \hat{x} \\
X_n \arrow[r] & X \arrow[d] & \widehat{X} = X' \arrow[l] & \supset U' \\
Y_n \arrow[r, hook] & Y & & \\
y & y' \arrow[l, no head] & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
F_n \arrow[r, "u_n"] \arrow[d, "\text{surj}"'] & i_{n*}(G_{U_n}) \\
G_n \arrow[ur] \arrow[r] & H_n
\end{tikzcd}

\begin{tikzcd}[row sep=small]
X \arrow[d, "f\ \text{de t.f.}"] \\
Y
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X' \arrow[r, no head] \arrow[d] & X \arrow[d, no head] \\
Y' \arrow[u] \arrow[ur] \arrow[r, no head] & Y
\end{tikzcd}

\begin{tikzcd}[row sep=small]
X \supset U \arrow[d] \\
S
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X \arrow[r, "\delta"] & Z \\
T_0 \arrow[u, "\varphi"] \arrow[r] & T \arrow[u, "u"'] \\
T_0^{(i)} \arrow[u] \arrow[r] & T^{(i)} \arrow[u, "u_i"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X \arrow[r] & Z \\
T_0 \arrow[u, no head] \arrow[r] & T \arrow[u]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X \arrow[d, no head] & X' \arrow[l, no head] \arrow[d, no head] & X'' \arrow[d, no head] & \\
Y & Y' \arrow[l] & Y'' \arrow[l] & Y'''  \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
F(Y) \arrow[r] & F(X') \arrow[r] \arrow[d] & F(X) \arrow[d] & \\
 & F(X' \times_Y X') \arrow[r] & F(X \times_Y X) \arrow[r] & F(X \times_{X'} X)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
F(X) \arrow[d] & F(Y) \arrow[l] \arrow[d] \\
F(X_{\mathrm{red}}) & F(Y_{\mathrm{red}}) \arrow[l]
\end{tikzcd}