\begin{tikzcd}[column sep=large]
E_0 \arrow[r, "\delta_0", bend left=18] & E_1 \arrow[l, "p_0"', bend left=18] \arrow[r, "\delta_1", bend left=18] & E_2 \arrow[l, "p_{12}"', bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
E_0 \arrow[r, "\delta_0", bend left=18] & E_1 \arrow[l, "p_0", bend left=18] \arrow[r, "\delta_1"', bend right=18] & E_2 \arrow[l, "p_{12}"', bend right=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
E_1 \arrow[r, "\delta_1", bend left=18] & E_2 \arrow[l, "p_{12}"', bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
F \times F \times F \arrow[d, "p_{12}", bend left=18] \arrow[d, "p_{13}"', bend right=18] \\
F \times F
\end{tikzcd}

\begin{tikzcd}[column sep=large, nodes={font=\scriptsize}]
U_{\gamma'} \arrow[r, "\varphi(v)"] & U_\gamma \times U_{\alpha_{n+1}} \arrow[r, "\varphi(u)\times\mathrm{id}"] & (U_{\alpha_0} \times \dots \times U_{\alpha_n}) \times U_{\alpha_{n+1}}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& \gamma \arrow[dl] \arrow[dr] & \\
\alpha_1 \arrow[dr] & & \alpha_2 \arrow[dl] \\
& \alpha_0 &
\end{tikzcd}

\begin{tikzcd}[column sep=large]
E_n \arrow[r, "\partial_n", bend left=18] & E_{n+1} \arrow[l, "k_n", bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
E^*_n \arrow[r, "d_n = k^*_n"', bend right=18] & E^*_{n+1} \arrow[l, "p_n = \partial^*_n"', bend right=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
C = X \arrow[r, "u = \varphi^*"', bend right=18] & C' = \widehat{A} \arrow[l, "v = \varphi_!"', bend right=18]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
I \arrow[r, "\text{épi}"] \arrow[dr, "\text{épi}"'] & J \\
& K
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
I \arrow[r] \arrow[d] & J \arrow[r] \arrow[d] & J' \arrow[d] \\
K \arrow[r] & L \arrow[r] & M
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_0 & X_1 \arrow[l] & X_2 \arrow[l] \\
X'_0 \arrow[u] & X'_1 \arrow[l] \arrow[u] & X'_2 \arrow[l] \arrow[u]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
I \arrow[r, hook] \arrow[d] & J = I \amalg K \arrow[d, no head] \\
I' \arrow[r, hook] & J' = I' \amalg K
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X(J) & X(I \amalg K) \arrow[l] \\
X(J') \arrow[u] & X(I' \amalg K') \arrow[l]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
E_n \arrow[r, "\partial_n"] & E_{n+1} \arrow[d, "k_{n-1}"] \\
& E_n
\end{tikzcd}

\begin{tikzcd}[column sep=large]
X_1 & X_2 \arrow[l, "p_0"', bend left=18] & X_3 \arrow[l, "p_{12}"', bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_3 \arrow[r, "p_1"] & X_2 \\
X_2 \arrow[u, "\delta_3"] & X_1 \arrow[l, "\delta_0"] \arrow[u, "\delta_0"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_2 & X_3 \arrow[l, "p_{12}"'] \\
X_1 \arrow[u, "k_1"] & X_2 \arrow[l, "\delta_1"] \arrow[u, "k'_2"']
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
E_2 \arrow[r, "\partial_2"] \arrow[d, "k_1"'] & E_3 \arrow[d, "k'_2"] \\
E_1 \arrow[r, "\partial_1"'] & E_2
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
E_3 \arrow[r, "k_2"] \arrow[d, "k'_2"'] & E_2 \arrow[d, "k_1"] \\
E_2 \arrow[r, "k_1"'] & E_1
\end{tikzcd}

\begin{tikzcd}[column sep=large]
X_2 \arrow[r, "\delta_2", bend left=18] & X_3 \arrow[l, "k_2", bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
X_1 & X_2 \arrow[r, "d", bend left=18] & X_3 \arrow[l, "p", bend left=18]
\end{tikzcd}

\begin{tikzcd}[column sep=large]
X^{*}_3 \arrow[r, "p^{*} = p|X^{*}_3"] & X_2
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_3 \arrow[r, "\delta_1"] & X_2 \arrow[d, "\delta_0"] \\
X_2 \arrow[u, "\delta_3"] \arrow[r, "\delta_0"'] & X_1 = \{e_1\}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
X_2 & X_3 \arrow[l, "p = \mathrm{pr}_2"'] \\
X_1 = \{e_1\} \arrow[u, "\kappa_1"] & X_2 \arrow[l, "p_1"] \arrow[u, "\kappa'_2"']
\end{tikzcd}

\begin{tikzcd}[column sep=large]
Y' \arrow[r, hook] \arrow[d, "\mathrm{can}\,\wr"'] & X' \arrow[d, "\wr"] \\
Y'\times\{z\} \arrow[r, hook, "\mathrm{id}_{Y'} \times i_{z,Z}"'] & Y'\times Z
\end{tikzcd}

\begin{tikzcd}[column sep=large]
\mathcal{V}^{*}_{Y,X} \arrow[r, "\text{bouchage de trous le long de } Y"] \arrow[d] & \mathcal{V}_{Y,X} \arrow[d] \\
X^{*} \arrow[r] & X
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathcal{V}^{*}_{Y,X} \arrow[r, hook] \arrow[d] & \mathcal{V}_{Y,X} \\
X^{*} &
\end{tikzcd}

\begin{tikzcd}[column sep=large, nodes={font=\scriptsize}]
\Pi_1\mathcal{V}^{*}_{Y,X} \arrow[r, "p"] \arrow[d, "i"'] & \Pi_1\mathcal{V}_{Y,X}\ (\simeq \Pi_1 Y) \arrow[d, dashed] \\
\Pi_1 X^{*} \arrow[r, dashed] & (\Pi_1 X)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\Pi_1(\mathcal{V}^{*}_{Y,X}) \arrow[r] \arrow[d] & \Pi_1(Y) \\
\Pi_1(X^{*}) &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\Pi_2(Y) \arrow[r] & \Pi_1(\mathcal{V}^{*}_{z,Z}) \arrow[r] & \Pi_1(\mathcal{V}^{*}_{Y,X}) \arrow[r] & \Pi_1(Y) \arrow[r] & \Pi_0(\mathcal{V}^{*}_{z,Z}) \arrow[d] \\
& & & & \Pi_0(\mathcal{V}^{*}_{Y,X}) \arrow[d] \\
& & & & \Pi_0(Y)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
1 \arrow[r] & \Pi_1(\mathcal{V}^{*}_{z,Z}) \arrow[r] & \Pi_1(\mathcal{V}^{*}_{Y,X}) \arrow[r] \arrow[d] & \Pi_1(Y) \arrow[r] & 1 \\
& & \Pi_1(X^{*}) & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
D^{*}_a \arrow[r, hook, "\text{« bouchage de trou en } a\text{ »}"] \arrow[d] & D_a \\
X^{*} = X \setminus \{a\} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathbb{Z}_{a,X} \arrow[r] \arrow[d] & \{1\} \\
\Pi_1(X^{*}) &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
D^{*}_0 \arrow[r] \arrow[d] & D_0 \\
\mathbb{C}^{*} &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
D^{*}_{\infty} \arrow[r, hook] \arrow[d] & D_{\infty} \arrow[d, dashed] \\
\mathbb{C} \arrow[r, dashed] & \mathbb{P}^1_{\mathbb{C}} \simeq S^2
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
\mathbb{Z} \arrow[r] \arrow[d] & 1 \\
1 &
\end{tikzcd}

\begin{tikzcd}[column sep=large, row sep=small]
& X_{\Delta_1} \arrow[dl, "\sigma"'] \arrow[dr, "b"] & \\
X_{\Delta_0} & & X_{\Delta_0}
\end{tikzcd}

\begin{tikzcd}[column sep=large, row sep=small, nodes={font=\scriptsize}]
X_{\Delta_2} \underset{\text{déf}}{=} (X_{\Delta_1}, b) \times_{X_{\Delta_0}} (X_{\Delta_1}, \sigma) \arrow[r] \arrow[d, hook] & X_{\Delta_1} \arrow[d, hook] \\
X_{\Delta_0} \times X_{\Delta_0} \times X_{\Delta_0} & X_{\Delta_0} \times X_{\Delta_0}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
& X_{\Delta_1} \arrow[dl, "\sigma"'] \arrow[dr, "b"] & \\
X_{\Delta_0} \arrow[dr, dashed] & & X_{\Delta_0} \arrow[dl, dashed] \\
& X &
\end{tikzcd}

\begin{tikzcd}[column sep=large, row sep=small]
& X_i^{*} \arrow[d, "\text{« âme »}"] \\
\mathcal{V}^{*}_{ij} \arrow[r] \arrow[d] & \mathcal{V}_{i,j} \\
X_j^{*} &
\end{tikzcd}

\begin{tikzcd}
  \mathcal{V}^{*}_{\Delta_1} \arrow[r, hook] \arrow[d]
    & \mathcal{V}_{\Delta_1} \arrow[d, dashed]
    & X^{*}_{\Delta_0} \arrow[l] \arrow[dl, dashed] \\
  X^{*}_{\Delta_0} & X &
\end{tikzcd}

\begin{tikzcd}
  \mathcal{V}^{*}_{i,j} \arrow[r] \arrow[d]
    & \mathcal{V}_{i,j} \arrow[d, dashed]
    & X^{*}_{i} \arrow[l] \arrow[dl, dashed] \\
  X^{*}_{j} & X &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & i' \arrow[r, no head] & j' & & X_{i'} \arrow[r, no head] & X_{j'} \\
  i \arrow[ur, no head] \arrow[dr, no head] & & & X_i \arrow[ur, no head] \arrow[dr, no head] & & \\
  & j & & & X_j &
\end{tikzcd}

\begin{tikzcd}
  {[i,j]}^{*} \arrow[r] \arrow[d] & {[i,j]} & i^{*} \arrow[l] \\
  {[j]}^{*} & &
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  X_0^{*} \arrow[r] & \mathcal{V}_{0,1} & \mathcal{V}^{*}_{0,1} \arrow[l] \arrow[d] & & & & & & \\
  & & X_1^{*} \arrow[r] & \mathcal{V}_{1,2} & \mathcal{V}^{*}_{1,2} \arrow[l] \arrow[d] & & & & \\
  & & & & X_2^{*} \arrow[r] & \mathcal{V}_{2,3} & \mathcal{V}^{*}_{2,3} \arrow[l] \arrow[d] & & \\
  & & & & & & X_3^{*} & & \\
  & & & & & & \cdots \arrow[d] & & \\
  & & & & & & X^{*}_{n-1} \arrow[r] & \mathcal{V}_{n-1,n} & \mathcal{V}^{*}_{n-1,n} \arrow[l] \arrow[d] \\
  & & & & & & & & X_n^{*}
\end{tikzcd}

\begin{tikzcd}[column sep=small, nodes={font=\scriptsize}]
  \mathcal{V}^{*}_{0,b} \arrow[r] \arrow[d] & \mathcal{V}_{0,b}
    & X_0^{*} \arrow[l] \arrow[r] & \mathcal{V}_{0,a}
    & \mathcal{V}^{*}_{0,a} \arrow[l] \arrow[d] \\
  X_b^{*} & & & & X_a^{*}
\end{tikzcd}

\begin{tikzcd}
  X_a^{*} \arrow[d] & & X_b^{*} \arrow[d] \\
  \mathcal{V}_{a,c} & & \mathcal{V}_{b,c} \\
  \mathcal{V}^{*}_{a,c} \arrow[u] \arrow[r] & X_c^{*} & \mathcal{V}^{*}_{b,c} \arrow[u] \arrow[l]
\end{tikzcd}

\begin{tikzcd}
  X_m^{*} \arrow[r] & \mathcal{V}_{m,m+1} & \mathcal{V}^{*}_{m,m+1} \arrow[l] \arrow[d] \\
  & & X^{*}_{m+1}
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  X_n^{*} \arrow[r] & \mathcal{V}_{n,n-1} & \mathcal{V}^{*}_{n,n-1} \arrow[l] \arrow[d] & & & & \\
  & & X^{*}_{n-1} \arrow[r] & \mathcal{V}_{n-1,n-2} & \mathcal{V}^{*}_{n-1,n-2} \arrow[l] \arrow[d] & & \\
  & & & & X^{*}_{n-2} & & \\
  & & & & \cdots \arrow[d] & & \\
  & & & & X_1^{*} \arrow[r] & \mathcal{V}_{1,0} & \mathcal{V}^{*}_{1,0} \arrow[l] \arrow[d] \\
  & & & & & & X_0^{*}
\end{tikzcd}

\begin{tikzcd}
  \mathcal{V}_{i',j',X'} \arrow[r, hook] & \mathcal{V}_{i',j'} \\
  \mathcal{V}^{*}_{i',j',X'} \arrow[r, hook] \arrow[u, hook]
    & \mathcal{V}^{*}_{i',j'} \arrow[u, hook]
\end{tikzcd}