\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\underline{\mathrm{Hom}}(\bar\Theta, C) \arrow[r, "\varphi^{*}"] & \underline{\mathrm{Hom}}(\Theta, C) \\
\underline{\mathrm{Hom}}_{\bar\delta}(\bar\Theta, C) \arrow[u, hook] & \underline{\mathrm{Hom}}_{\delta}(\Theta, C) \arrow[u, hook]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
C \arrow[r, "F"] & C' \arrow[r, "G"] & C'' \\
\Theta \arrow[u, "u"] & J' \arrow[l, "g'"'] & \\
\bar{I}' \arrow[u, "\xi'"] & \bar{I}'' \arrow[ul, "\xi''"'] & J'' \arrow[ull, "g''"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
R_{0} \arrow[r] & R_{1} \arrow[r, "\mathrm{loc}"] & R_{2} \arrow[r, "\mathrm{loc}"] & R_{3} = R \\
J_{0} \arrow[u] \arrow[r, "\text{bij. sur objets}"] & J_{1} \arrow[u] \arrow[r, "\mathrm{loc.}"] & J_{2} \arrow[u] \arrow[ur] & \\
I \arrow[u] & & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\hat{J_{1}} \arrow[r, "\mathrm{loc.}"] \arrow[d, "\mathrm{loc}"'] & \hat{J_{2}} \arrow[r] \arrow[d, "\mathrm{loc}"] & R \\
R_{1} \arrow[r, "\mathrm{loc}"] & R_{2} \arrow[r, "\mathrm{loc}"] & R_{3}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & R & & \\
R^{+} \arrow[ur, no head] & & V = \overline{(\varphi_{0},\varphi_{1})} \arrow[ul, no head] & \\
 & R^{+} \wedge V = \varphi_{1} \arrow[ul, no head] \arrow[ur, no head] & & \overline{(\varphi_{0})} \arrow[ul, no head] \\
 & & \emptyset \arrow[ul, no head] \arrow[ur, no head] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & x_{1} & \\
x \arrow[r, "i_{c}"] & \bar{x}_{c} \arrow[u, "q_{1}"] \arrow[r, "q_{2}"] \arrow[d, "q_{3}"'] & x_{2} \\
 & x_{3} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & B \arrow[dl] \arrow[dd, "f"] \\
B_{\pi} \arrow[dr] & \\
 & B'
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
B \arrow[d, "f_{*}", bend left=25] \\
B' \arrow[u, "f^{*}", bend left=25]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\simeq B \arrow[d, "f"] & B \arrow[d, "f_{*}", bend left=25] \\
B' & B' \arrow[u, "f^{*}", bend left=25]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
 & \text{anneau} & & \\
\text{anneau local} \arrow[ur] & & \text{anneau réduit} \arrow[ul] & \text{spectre compact} \arrow[l] \\
\text{anneau str. local} \arrow[u] & & \text{anneau intègre} \arrow[u] & \text{pseudocorps} \arrow[ul] \arrow[u] \\
 & & \text{corps} \arrow[u] \arrow[ur] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
D \arrow[d] \arrow[r, hook] & A \times A \arrow[d, "(x{,}y) \mapsto xy"] \\
e \arrow[r, "0"] & A
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
D_{N} \arrow[d] \arrow[r, hook] & A \times A \arrow[d, "(x{,}y) \mapsto xy"] \\
N \arrow[r, hook] & A
\end{tikzcd}

\begin{tikzcd}
\underline{\mathrm{Hom}}'(R_{\Lambda}, \mathrm{Ens}) \arrow[r, hook] &
\underline{\mathrm{Hom}}'(R, \mathrm{Ens}) \\
(\Lambda\text{-alg}) \arrow[u, "\wr"] \arrow[r, hook] &
(\mathrm{Ann}) \arrow[u, "\wr"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
    A \times \Pi_{n} \arrow[d] & A_{j} \arrow[dl] \\
    A_{\Pi_{n}} \arrow[d, Rightarrow] & \\
    \Pi_{n} &
    \end{tikzcd}

\begin{tikzcd}
\mathcal{C} \arrow[r, "\varphi"] & E \arrow[r, "\hat{\varphi}"] \arrow[dr, dashed] & \hat{\mathcal{C}} \\
& & \hat{E} \arrow[u, dashed, "\hat{\varphi}^{*}"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
  \text{Thé}_{\Delta'} \arrow[rr, "\text{restriction}"] \arrow[d] & & \text{Thé}_{\Delta} \arrow[d] \\
  \mathrm{Thal}_{\Delta'} \arrow[rr, "\text{restr.}"] \arrow[d, no head, "\wr\|" description] & & \mathrm{Thal}_{\Delta} \arrow[d, no head, "\wr\|" description] \\
  \Delta'_{\mathrm{al}} \arrow[rr] & & \Delta_{\mathrm{al}}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  \mathrm{Th}_{\Delta'} \arrow[rrr] \arrow[dr] \arrow[dd, bend right=20] & & & \mathrm{Th}_{\Delta} \\
  & \mathrm{Thal}_{\Delta'} \arrow[rrr] & & & \mathrm{Thal}_{\Delta} \arrow[ul] \arrow[dd, bend left=20] \\
  \Delta' \arrow[rrr] \arrow[uu, bend right=20] & & & \Delta \\
  & \Delta'_{\mathrm{al}} \arrow[ul] \arrow[uu] \arrow[rrr] & & & \Delta_{\mathrm{al}} \arrow[ul] \arrow[uu, bend left=20]
\end{tikzcd}

\begin{tikzcd}
  T(C) \arrow[r, hook] \arrow[d] & T(C') \arrow[d] \\
  T'(C) \arrow[r, hook] & T'(C')
\end{tikzcd}

\begin{tikzcd}[column sep=small]
          T(C) \arrow[r] \arrow[d] & \mathrm{Hom}_{\mathrm{Cat}}(C^{\circ}, T(\mathrm{Ens})) \arrow[d, "\varphi \mapsto (\tilde{r}_{i} \circ \varphi)"] \\
          C^{I} \arrow[r] & \mathrm{Hom}_{\mathrm{Cat}}(C^{\circ}, (\mathrm{Ens}))^{I}
        \end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
  & \tilde{I}' \arrow[dr] \arrow[ddl] & \\
  I' \arrow[ur] \arrow[rr] \arrow[d, "\text{pl. fid.}"'] & & \bar{I}' \arrow[d, "\text{ess. surj., et surjectif sur les Hom}"] \\
  R & & \rho(R) \arrow[ll, hook']
\end{tikzcd}

\begin{tikzcd}[column sep=large]
  \text{Thé}_{\Delta} \arrow[r, bend left=20, "\rho"] & \Delta \arrow[l, bend left=20, "\sigma"']
\end{tikzcd}

\begin{tikzcd}
  e \sqcup O^{*} \arrow[r, "\varphi"] \arrow[d, "j"'] & O \\
  D \arrow[ur, "i"'] &
\end{tikzcd}

\begin{tikzcd}
  T_{\lambda} \arrow[rr, "u"] \arrow[dr, "b^{T}_{\lambda}"'] & &
  T'_{\lambda} \arrow[dl, "b^{T'}_{\lambda}"] \\
  & \tau^{I} &
\end{tikzcd}

\begin{tikzcd}
  T(C) \arrow[r] \arrow[d] & T(C') \arrow[d] \\
  C^{I} \arrow[r, hook] & C'^{I}
\end{tikzcd}

\begin{tikzcd}
  T(C) \arrow[r] \arrow[d] & T(\hat{C}) \arrow[d] \\
  C^{I} \arrow[r] & \hat{C}^{I}
\end{tikzcd}

\begin{tikzcd}[column sep=large]
  T(\hat{C}) \arrow[r, "\alpha\ \approx"] \arrow[d, "b_{\hat{C}}"'] &
  \mathrm{Hom}(C^{\circ}, S_{T})
  \arrow[d, "{\mathrm{Hom}(C^{\circ},\, b_{(\mathrm{Ens})})}"] \\
  \hat{C}^{I} \arrow[r, "\cong"'] & \mathrm{Hom}(C^{\circ},
  (\mathrm{Ens}))^{I}
\end{tikzcd}

\begin{tikzcd}[column sep=large]
  T(C) \arrow[r, hook] \arrow[d, "b_{C}"'] & \mathrm{Hom}(C^{\circ},
  S_{T}) \arrow[d, "{\varphi \mapsto (b_{i,\mathrm{Ens}} \circ
  \varphi)_{i \in I}}"] \\
  C^{I} \arrow[r, hook] & \hat{C}^{I}
\end{tikzcd}

\begin{tikzcd}
  B \arrow[dr, "b"'] & & X \arrow[dl] \\
  & \widehat{(\mathrm{Ens}_{f})^{\circ}}{}^{I} = B_{I} &
\end{tikzcd}