\begin{tikzcd}[column sep=small, row sep=small]
  Z \arrow[r, "f"] & X & X' \arrow[l, "p"'] & Z' \arrow[l, "f'"'] \\
  k \arrow[rr, no head] & & k' &
\end{tikzcd}

\begin{tikzcd}
  X_{\bar k} \arrow[d] \\
  I_{\bar k}
\end{tikzcd}

\begin{tikzcd}
  X \arrow[d, "f"] \\
  T
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
  X \arrow[d] & X' \arrow[d, no head] \\
  T \arrow[d] & T' \arrow[d, no head] \\
  S = \mathrm{Spec}\,k \arrow[r, no head] & S'
\end{tikzcd}

\begin{tikzcd}
  X \times Y \arrow[r, "\alpha_X \times \alpha_Y"] \arrow[dr, "\pi_{X \times Y}"'] & \mathrm{Dist}(X) \times \mathrm{Dist}(Y) \arrow[d, "\pi_{X,Y}"] \\
  & \mathrm{Dist}(X \times Y)
\end{tikzcd}

\begin{tikzcd}
  M_A \arrow[r, "u"] \arrow[d, "g \otimes \mathrm{id}_M"'] & M_A \arrow[d, "g \otimes \mathrm{id}_M"] \\
  M_{k'} \arrow[r, "g_M"'] & M_{k'}
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] \arrow[d, "\mathrm{can}"'] & M \otimes A \arrow[d, "\mathrm{id}_M \otimes g"] \\
  M \otimes k' \arrow[r, "g_M"'] & M \otimes k'
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] \arrow[dr, "g^{\circ}_M"'] & M \otimes A \arrow[d, "\mathrm{id}_M \otimes g"] \\
  & M \otimes k'
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] \arrow[dr, "="'] & M \otimes A \arrow[d, "\mathrm{id}_M \otimes \varepsilon"] \\
  & M
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] \arrow[dr, "(gg')^{\circ}_M"'] & M \otimes A \arrow[d, "\mathrm{id}_M \otimes \pi"] \\
  & M \otimes A \otimes A
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] & M \otimes A \arrow[d] \\
  & M \otimes A \otimes A
\end{tikzcd}

\begin{tikzcd}
  M \arrow[d, "u_0"'] & \\
  M \otimes A \arrow[r, "u_0 \otimes \mathrm{id}_A"] & M \otimes A \otimes A
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "u_0"] \arrow[d, "u_0"'] & M \otimes A \arrow[d, "\mathrm{id}_M \otimes \pi"] \\
  M \otimes A \arrow[r, "u_0 \otimes \mathrm{id}_A"'] & M \otimes A \otimes A
\end{tikzcd}

\begin{tikzcd}
  M \arrow[r, "\omega_M"] \arrow[d] & M \otimes A \arrow[d, "g \otimes \mathrm{id}_A"] \\
  N' \arrow[r, "\omega_{N'}"'] & N' \otimes A
\end{tikzcd}

\begin{tikzcd}
  M'' \arrow[r, "u_{M''}\,?"] \arrow[d, hook, "i"'] & M'' \otimes A \arrow[d, "i \otimes \mathrm{id}_A"] \\
  M \arrow[r, "u_M"'] & M \otimes A
\end{tikzcd}

\begin{tikzcd}
  G \arrow[r, "\mathrm{id}_G \times \sigma"] \arrow[dr, "p"'] & G \times G \arrow[r, "\pi"] & G \\
  & e \arrow[ur, "\varepsilon"'] &
\end{tikzcd}

\begin{tikzcd}
  A & A \otimes A \arrow[l] & A \arrow[l, "\pi"'] \arrow[dl, "\varepsilon"] \\
  & k \arrow[ul, "p"] &
\end{tikzcd}