\begin{tikzcd}[column sep=small, row sep=small]
 & SRT(X) \arrow[d, no head, "\mathfrak{S}_I"] & \\
 & \mathbf{R}^{I}\cdot S_{*}T^{!} \arrow[dl, no head, "T^{!}"'] \arrow[dr, no head, "\mathbb{U}^{I}"] & \\
\mathbf{R}^{I} \arrow[dr, no head, "\mathbb{U}^{I}"'] & & S_{*}T^{!}(X) \arrow[dl, no head, "T^{!}(X)"] \\
 & \mathbf{Z}^{I} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathbf{R}^{I} \arrow[dr] & \\
 & SRT(X) \\
S_{*}T^{!}(X) \arrow[ur] &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
1 \arrow[r] & \mathcal{T}^{!}_{0,4} \arrow[r] \arrow[d, no head, "\wr"'] & \mathcal{T}_{0\,4} \arrow[r] \arrow[d] & \mathfrak{S}_4 \arrow[r] \arrow[d] & 1 \\
1 \arrow[r] & \pi_{0,3} \arrow[r] & \mathcal{T}'_{0\,4} \arrow[r] & \mathfrak{S}_3 \arrow[r] & 1 \\
1 \arrow[r] & \pi_{0,3}(2,\mathbf{Z}) \arrow[r] \arrow[u, no head, "\wr"] & \mathcal{T}_{1,1} \arrow[r] \arrow[u] & \widetilde{\mathfrak{S}}_3 \arrow[u]
\end{tikzcd}

\begin{tikzcd}
E_{\varepsilon,+} \arrow[r, leftrightarrow] \arrow[d, leftrightarrow] & E_{\varepsilon,-} \arrow[d, leftrightarrow] \\
E_{Q} \arrow[r] & E_{H}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
R = RR/\sigma_1 \arrow[d] & RR \arrow[l] \arrow[d, "\mathrm{supp}"] & \\
A = \vec{A}/\sigma & \vec{A} \arrow[l] \arrow[r, leftrightarrow] & \vec{A}_0 \arrow[d, "\sigma"] \\
 & & S \arrow[r, "g"] & N
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & \mathcal{T} \arrow[dl, no head] \arrow[dr, no head] & \\
S\mathcal{T} \arrow[dr, no head] & & D\mathcal{T} \arrow[dl, no head] \\
 & SD\mathcal{T} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & \mathbb{L} \arrow[dl, no head] \arrow[dr, no head] & \\
S\mathbb{L} \arrow[dr, no head] & & d\mathbb{L} \arrow[dl, no head] \\
 & Sd\mathbb{L} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & \mathcal{T} \arrow[dl, no head] \arrow[dr, no head] \arrow[rrrr] & & & & \mathbb{L} \arrow[dl, no head] \arrow[dr, no head] & \\
S\mathcal{T} \arrow[dr, no head] \arrow[rr, no head] & & D\mathcal{T} \arrow[dl, no head] \arrow[rr] \arrow[rrrr, bend right=20] & & S\mathbb{L} \arrow[dr, no head] & & d\mathbb{L} \arrow[dl, no head] \\
 & SD\mathcal{T} \arrow[rrrr] & & & & Sd\mathbb{L} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
 & \mathbb{T}_{\mathrm{top}} \\
\mathbb{T}'_{\mathrm{diff}} \arrow[r, leftrightarrow] & \mathbb{T}_{\mathrm{diff}} \arrow[u] \\
\mathbb{T}'_{\mathrm{an}} \arrow[r, leftrightarrow] & \mathbb{T}_{\mathrm{an}} \arrow[u] \\
\mathbb{T}'_{\mathrm{hyp}} \arrow[u] \arrow[r, leftrightarrow] & \mathbb{T}_{\mathrm{hyp}} \arrow[u] \\
 & \mathbb{T}_{\mathbf{C}\text{-alg}} \arrow[u] \\
 & \mathbb{T}_{\overline{\mathbf{Q}}\text{-alg}} \arrow[u] \\
 & \mathbb{T}_{\mathrm{comb}} \arrow[u] \\
 & \mathbb{T}_{\mathrm{Lego}} \arrow[u] \\
 & \mathbb{T}_{\mathbb{P}} \arrow[u]
\end{tikzcd}

\begin{tikzcd}
S_{*}\mathcal{T}D_{\mathrm{top}} \arrow[r, hook] & S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}} \arrow[r] & {[\pm 1]}
\end{tikzcd}

\begin{tikzcd}
\vec{A} \arrow[d] & = & \vec{A}_0 \arrow[d, "\deg 2"] & \sqcup & \vec{A}_{\ell} \arrow[d, "\deg 1"] \\
\widetilde{A} & = & A & \sqcup & A_{\ell}
\end{tikzcd}

\begin{tikzcd}
A \ (= \vec{A} \setminus \vec{A}^{\sigma}) \arrow[d] \arrow[r, "r"] & \mathbf{N} \\
S \arrow[r, "\gamma"] & \mathbf{N}
\end{tikzcd}

\begin{tikzcd}
A = A_0 \arrow[d] & \\
S \arrow[r, "\gamma"] & \mathbf{N}
\end{tikzcd}

\begin{tikzcd}
\vec{R}^{+}_{\ell} \arrow[r, hook] & \vec{R} \arrow[r] & \vec{A} \arrow[d, "o"'] \\
 & & S \arrow[r, "\gamma"] & \mathbf{N}
\end{tikzcd}

\begin{tikzcd}
S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}}\ (\text{à sous-ens.\ marqué $R'$ de sommets-repères}) \arrow[d] \\
S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}}
\end{tikzcd}

\begin{tikzcd}
S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}}(R'\ \text{marqué}) \arrow[r, "\text{gommage de } R'"] & S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}}
\end{tikzcd}

\begin{tikzcd}[column sep=small]
S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}}(\ldots R' \ldots) \arrow[r, "\text{gommage de } R'"] \arrow[d, "\text{oubli du marquage } R'"'] & S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}} \arrow[d] \\
S_{*}\mathcal{T}D^{\pm}_{\mathrm{top}} \arrow[r] & (\mathrm{Gra.bipond})
\end{tikzcd}

\begin{tikzcd}
S_1\mathcal{T}^{\pm}_{g,\nu} \arrow[r] & \mathcal{T}^{\pm}_{g,\nu} \arrow[r] & (\mathrm{Ens}(\nu) \times [\pm 1])
\end{tikzcd}

\begin{tikzcd}
(**)\quad S\mathcal{T}^{\pm}_{g,\nu,\nu'} \arrow[r] & S\mathcal{T}_{g,\nu\,?\,\nu'}
\end{tikzcd}

\begin{tikzcd}[column sep=large]
{[\pm 1]} & {[\pm 1]} \\
\mathcal{T}^{\pm}_{\mathrm{top}} \arrow[u] \arrow[r, hook, "\mathrm{imm}"] & S\mathcal{T}S^{\pm}_{\mathrm{top}} \arrow[u] \\
\mathcal{T}_{\mathrm{top}} \arrow[u, "{\text{fid.\ ess.\ surj.}}"] \arrow[r, hook, "\mathrm{imm}"] & \mathcal{T}S_{\mathrm{top}} \arrow[u, "{\text{fid.\ ess.\ surj.}}"']
\end{tikzcd}