\begin{tikzcd}
\underline{\mathfrak{g}}^{\mathrm{rss}} \arrow[d] &
\underline{\mathfrak{L}}^{\mathrm{rss}}\simeq\mathrm{Kill}\times\underline{t}^{\mathrm{rs}} \arrow[l] \arrow[d] \\
\mathrm{Tor} & \mathrm{Kill} \arrow[l]
\end{tikzcd}

\begin{tikzcd}
\underline{\mathfrak{g}}^{\mathrm{rss}} \arrow[d, "f^{\mathrm{rss}}"'] &
\underline{\mathfrak{L}}^{\mathrm{rss}} \arrow[l, "q^{\mathrm{rss}}"'] \arrow[d, "\tilde f'^{\mathrm{rss}}"] \\
\mathfrak{J}^{\mathrm{rs}}=\underline{t}^{\mathrm{rss}}/W &
\mathfrak{J}'=\underline{t}^{\mathrm{rss}} \arrow[l]
\end{tikzcd}

\begin{tikzcd}
\underline{\mathfrak{g}} \arrow[d, "f"'] & & \underline{\mathfrak{L}} \arrow[ll, "q"'] \arrow[dl, "\tilde f'"] \\
\mathfrak{J}=\underline{t}/W & \mathfrak{J}'=\underline{t} \arrow[l] &
\end{tikzcd}

\begin{tikzcd}
\underline{\mathfrak{g}} \arrow[d, "f"'] & \underline{\mathfrak{g}}' \arrow[l] \arrow[d, "f'"'] & \underline{\mathfrak{L}} \arrow[l, "p"'] \arrow[dl, "\tilde f'"] \arrow[r] \arrow[ll, bend right=30, "q"'] & D \\
\mathfrak{J} & \mathfrak{J}' \arrow[l] & &
\end{tikzcd}

\begin{tikzcd}
\mathfrak{X}=G \arrow[d, "f"'] & \mathfrak{X}'=G' \arrow[l] \arrow[d, "f'"] & \mathfrak{B}=\tilde{\mathfrak{X}} \arrow[l, "p"'] \arrow[dl, "\tilde f"] \\
I & I'=T \arrow[l, "\pi"] &
\end{tikzcd}

\begin{tikzcd}
G'^{\mathrm{reg}} \arrow[d, hook] & \mathfrak{B}^{\mathrm{reg}} \arrow[l] \arrow[d, hook] \\
G' \arrow[d] & \mathfrak{B} \arrow[l] \\
S \arrow[u, bend left=40] & D \arrow[u, hook] \arrow[ul] \arrow[l]
\end{tikzcd}

\begin{tikzcd}
\mathrm{ST}_c\simeq(\mathrm{CL})_{c'} \arrow[d] & \mathrm{Dyn}_c \arrow[l] \arrow[d] \\
\underline{\varnothing}_c\simeq\mathrm{Par}_{c'} & \mathrm{Un}_c \arrow[l]
\end{tikzcd}

\begin{tikzcd}
L \arrow[d] & Z_0 \arrow[l] \arrow[d] \\
P & \mathfrak{z}(e) \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & & 0 \arrow[dl, no head] \arrow[dr, no head] & & \\
  & \mathfrak{z} \arrow[dr, no head] & & \mu \arrow[dl, no head] & \\
  & & \mu \times \mathfrak{z} \arrow[dl, no head, "T/\mu"'] \arrow[dd, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] \arrow[dr, no head] & & \\
  & \mathfrak{z}\cdot T \arrow[dl, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"'] & & \mu \cdot T' \arrow[dr, no head] & \\
  N(\mu) \arrow[rr, no head] \arrow[d, no head] & & N \cap N' \arrow[rr, no head] & & N' \\
  N & & & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & & & \text{Kost-Kill-norma} \arrow[dl, no head] \arrow[dr, no head] & & & \\
  & & \text{C Kost norma} \arrow[dr, no head] & & \text{Kost Kill} \arrow[dl, no head] & & \\
  & & & \text{C Kos} \arrow[dl, no head] \arrow[ddd, no head] \arrow[dr, no head, "\wr^{*}"] \arrow[drr, no head] & & & \\
  & & \text{E Kos} \arrow[dl, no head] \arrow[d, no head, "\wr^{**}"] & & \text{C Cox} \arrow[dll, no head] \arrow[ddl, no head, "{}^{*}"] \arrow[dr, no head] & \text{D Cy} \arrow[d, no head, "\wr^{**}"] \arrow[dr, no head] & \\
  & \text{SG Kos} \arrow[dl, no head] \arrow[dr, no head, "\wr^{*}"] & \text{E Cox} \arrow[d, no head] & & & \text{P Cox} \arrow[dr, no head] & \text{Tor} \arrow[d, no head, "="] \\
  \text{Tor} \arrow[dr, no head, "="'] & & \text{SG Cox} \arrow[r, no head, "{}^{*}"] & \text{Toapp} \arrow[rrr, no head, "{}^{*}"'] & & & \text{Tor} \\
  & \text{Tor} \arrow[ur, no head] & & & & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  T \arrow[r, no head, "\mathfrak{z}"] \arrow[d, no head, "T/\mu"'] & \mathfrak{z}(\mu) \arrow[r, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] \arrow[d, no head, "T/\mu"] & N(\mu) \arrow[r, no head] \arrow[d, no head, "T/\mu"] & N \arrow[d, no head] & \\
  T \cap N' \arrow[r, no head, "\mathfrak{z}"] \arrow[d, no head, "0"'] & \mathfrak{z}(\mu) \cap N' \arrow[r, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] \arrow[d, no head, "0"] & N(\mu) \cap N' \arrow[r, no head, "="] \arrow[d, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] & N \cap N' \arrow[r, no head] \arrow[d, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] & N' \arrow[d, no head] \\
  T \cap N(D) \arrow[r, no head, "\mathfrak{z}"] \arrow[d, no head, "\mu"'] & \mathfrak{z}(\mu) \cap N(D) \arrow[r, no head, "0"] \arrow[d, no head, "\mu"] & N(\mu) \cap N(D) \arrow[r, no head, "="] \arrow[d, no head, "\mu"] & N \cap N(D) \arrow[r, no head, "T'/\mathfrak{z}"] \arrow[d, no head, "\mu"] & N(D) = \mu \cdot T' \arrow[d, no head, "\mu"] \\
  T \cap T' \arrow[r, no head, "\mathfrak{z}"] & \mathfrak{z}(\mu) \cap T' \arrow[r, no head, "="] & N(\mu) \cap T' \arrow[r, no head, "="] & N \cap T' \arrow[r, no head, "T'/\mathfrak{z}"] & T'
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  T \arrow[r, no head] \arrow[d, no head] & T \cdot \mathfrak{z} \arrow[r, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"] \arrow[d, no head] & N(\mu) \arrow[r, no head] \arrow[d, no head] & N \arrow[d, no head] & \\
  \mu \arrow[r, no head] \arrow[d, no head] & \mu \times \mathfrak{z} \arrow[r, no head, "(\mathbb{Z}/h\mathbb{Z})^{*}"'] \arrow[d, no head] & N(\mu) \cap N' \arrow[r, no head, "="] & N \cap N' \arrow[r, no head] & N' \\
  0 \arrow[r, no head] & \mathfrak{z} & & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  T \arrow[r, no head, "\mathfrak{z}"] \arrow[d, no head] & \mathfrak{z}(\gamma) \arrow[r, no head] \arrow[d, no head] & N(T) \arrow[r, no head] \arrow[d, no head] & G \arrow[d, no head] \\
  T \cap N(T') \arrow[r, no head, "\mathfrak{z}"] \arrow[d, no head, "\mathbb{Z}/h\mathbb{Z}"] & \mathfrak{z}(\gamma) \cap N(T') = N'^{\gamma} \arrow[r, no head] \arrow[d, no head, "\mathbb{Z}/h\mathbb{Z}"] & N(T) \cap N(T') \arrow[r, no head] \arrow[d, no head] & N(T') \arrow[d, no head, "W'"] \\
  T \cap T' \arrow[r, no head, "\mathfrak{z}"] & \mathfrak{z}(\gamma) \cap T' = T'^{\gamma} \arrow[r, no head, "="] & N(T) \cap T' \arrow[r, no head] & T'
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & & \underline{\mathrm{Isom}}(G_0, G) \arrow[d, no head, "\wr"] \arrow[r, dashed] & \underline{\mathrm{Hom}}_{\mathrm{gr}}(\mathrm{Sl}(2), G) & \\
  & & \text{SSPEP} \arrow[dl, no head] \arrow[d, no head] \arrow[dr, no head] & & \\
  & \text{SSPTor}_0 \arrow[r, no head, "\simeq"] \arrow[d, no head] \arrow[dl, no head] & \text{SSPKill} \arrow[dl, no head] \arrow[dr, no head] & \text{SSPBorep} \arrow[d, no head] \arrow[r, no head] & \text{SAP}_0 \simeq \text{EUP} \arrow[d, no head] \\
  \text{Kill} \simeq \text{ST}_0\text{P} \arrow[d, no head] & \text{SSPTor} \arrow[dr, no head] \arrow[dl, no head] & & \text{SSPBor} \arrow[dl, no head] \arrow[r, no head] & \text{SAP} \\
  \text{STP} & & \text{SSP} & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & & & e \arrow[dl, no head, "1"'] \arrow[d, no head, "1"] \arrow[dr, no head, "1"] & \\
  & & t \arrow[dl, no head, "r-1"'] \arrow[d, no head] \arrow[r, no head, "="] & t \arrow[dl, no head] \arrow[dr, no head, "1"] & b_u \arrow[d, no head, "1"] \arrow[dr, no head, "r-1"] & \\
  N_1 \arrow[r, no head, "\circ"] \arrow[d, no head] & T \arrow[d, no head, "\mathbb{Z}/2\mathbb{Z}"] & n \arrow[dr, no head, "2"'] \arrow[dl, no head, "r-1"'] & & b \arrow[dl, no head, "1"] \arrow[dr, no head, "r-1"] & Z(b_u) \arrow[d, no head, "1(\mathbb{G}_m)"] \\
  N \arrow[r, no head] & N_0 & & H & & N(b_u)
\end{tikzcd}