\begin{tikzcd}
X \arrow[rr, "f"] \arrow[dr, "p"'] & & Y \arrow[dl, "q"] \\
& S &
\end{tikzcd}

\begin{tikzcd}
X \arrow[d, "f"'] & X' \arrow[l, "h"'] \arrow[d, "f'"] \\
Y & Y' \arrow[l, "g"]
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, "f"] & Y \\
Z_i \arrow[u, "u_i"] \arrow[ur, "f_i"'] &
\end{tikzcd}

\begin{tikzcd}
H^r(X) \arrow[dr, "u_i^{*}"'] & & H^r(Y) \arrow[ll, "f^{*}"'] \\
& H^r(Z_i) \arrow[ur, "f_{i*}"'] &
\end{tikzcd}

\begin{tikzcd}[column sep=large]
f^{*}(G)(\supplied{-}p)[\supplied{-}2p] \arrow[r] \arrow[dr, bend right=20] &
Rf^{!}(G) \\
& Rf^{!}(A_Y) \overset{L}{\otimes} f^{*}(G) \arrow[u]
\end{tikzcd}

\begin{tikzcd}
\bullet \arrow[d, "f_{!}"'] & \circledcirc \arrow[l, "g^{*}"'] \arrow[d, "f_{!}"] & \bullet \arrow[r, "g_{*}"] & \bullet \\
\circledcirc & \bullet \arrow[l, "g^{*}"] & \bullet \arrow[u, "f^{!}"] \arrow[r, "g_{*}"'] & \bullet \arrow[u, "f^{!}"']
\end{tikzcd}

\begin{tikzcd}
X' \arrow[r, "g'"] \arrow[d, "f'"'] & X \arrow[d, "f"] \\
S' \arrow[r, "g"] & S
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=large, nodes={font=\scriptsize}]
\operatorname{Hom}(K, R\underline{\operatorname{Hom}}_{\mathcal{A}}(f^{*}L, Rf^{!}M)) \arrow[r, "(1)"] \arrow[d, leftrightarrow, "\wr"'] & \operatorname{Hom}(K, Rf^{!}R\underline{\operatorname{Hom}}_{\mathcal{A}}(L, M)) \arrow[r, leftrightarrow, "\sim\ \mathrm{adj.}"] & \operatorname{Hom}(Rf_{!}K, R\underline{\operatorname{Hom}}_{\mathcal{A}}(L, M)) \arrow[d, leftrightarrow, "\wr"] \\
\operatorname{Hom}(K \otimes^{L}_{\mathcal{B}} f^{*}L, Rf^{!}M) \arrow[r, leftrightarrow, "\sim\ \mathrm{adj}"'] & \operatorname{Hom}(Rf_{!}(K \otimes^{L} f^{*}L), M) \arrow[r, "(2)"'] & \operatorname{Hom}(Rf_{!}K \otimes^{L} L, M)
\end{tikzcd}

\begin{tikzcd}
D^{+}(X, f^{*}\mathcal{A}) \arrow[r, "u."] & D^{+}(X, f^{*}\mathcal{B}) \\
D^{+}(S, \mathcal{A}) \arrow[r, "u."] \arrow[u, "Rf^{!}"] & D^{+}(S, \mathcal{B}) \arrow[u, "Rf^{!}"']
\end{tikzcd}

\begin{tikzcd}
X \arrow[r, hook, "j"'] \arrow[d, "f"'] & \bar X \arrow[dl, "\bar f"] \\
S &
\end{tikzcd}

\begin{tikzcd}
\bar X \arrow[d, no head] \arrow[dd, bend right=50, "\bar f"'] & \bar X_V \arrow[d, no head] \arrow[dd, bend right=50, "\bar f_V"'] & \\
X \arrow[d, "f"'] & X_V \arrow[l] \arrow[d, "f_V"] & U \arrow[l] \\
S & V \arrow[l, "j"] &
\end{tikzcd}

\begin{tikzcd}
X \arrow[d, "f"'] & X \times_S X \arrow[l, "p_1"'] \arrow[d, "p_2"] & X \arrow[l, "\Delta"'] \\
S & X \arrow[l, no head, "f"] &
\end{tikzcd}