\begin{tikzcd}
  A \times Y \arrow[dr, "t"'] & A \times X \arrow[l, "i'"'] \arrow[d, "s"] \\
  & A
\end{tikzcd}

\begin{tikzcd}[row sep=small]
  A \times Y \arrow[r, "p"] & Y \\
  \parallel & \\
  A \times A \times P \arrow[r] & A \times P
\end{tikzcd}

\begin{tikzcd}
X \times T & X \times T \times T' \arrow[l] \arrow[d, no head] \\
T \arrow[u, no head] & T \times T' \arrow[l]
\end{tikzcd}

\begin{tikzcd}
X \arrow[r] & Y \\
X \times T \arrow[r] \arrow[d] & Y \times T \arrow[dl] \\
T &
\end{tikzcd}

\begin{tikzcd}
Y \arrow[r] & A^{1}_{Y} \arrow[r, "N"] & A^{N}_{Y}
\end{tikzcd}

\begin{tikzcd}
  H^{1}(Y) \arrow[r] & H^{1}(X) \\
  H^{1}(A_Y) \arrow[u, "\varphi_Y"] \arrow[r] & H^{1}(A_X) \arrow[u, "\varphi_X"'] \\
  A_Y & A_X \arrow[l]
\end{tikzcd}

\begin{tikzcd}
  H^{2m-1}(Y)(m-1) \arrow[r] \arrow[d, "\psi_Y"'] & H^{2n-1}(X) \arrow[d, "\varphi_X"] \\
  H^{1}(B_Y) \arrow[r] & H^{1}(B_X) \\
  B_Y & B_X \arrow[l]
\end{tikzcd}

\begin{tikzcd}
  H^{2m-1}(Y)(m-1) \arrow[r] \arrow[d, "\psi_Y"'] & H^{1}(X) \\
  H^{1}(B_Y) \arrow[r] & H^{1}(A_X) \arrow[u, "\varphi_X"'] \\
  B_Y & A_X \arrow[l]
\end{tikzcd}

\begin{tikzcd}
  H^{1}(Y) \arrow[r] & H^{2n-1}(X)(n-1) \arrow[d, "\psi_X"] \\
  H^{1}(A_Y) \arrow[u, "\varphi_Y"] \arrow[r] & H^{1}(B_X) \\
  A_Y & B_X \arrow[l]
\end{tikzcd}

\begin{tikzcd}
  H^{1}(X) \arrow[r, "a(\gamma^{n}(Z))"] & H^{1}(Y) \\
  H^{1}(A_X) \arrow[u, "\varphi_X^{*}"] \arrow[r, "u_Z^{(1)}"] & H^{1}(A_Y) \arrow[u, "\varphi_Y^{*}"']
\end{tikzcd}

\begin{tikzcd}
  H^{1}(A_Y) \arrow[r, "u^{(1)}"] \arrow[d, "\varphi_Y^{(1)}"'] & H^{1}(B_X) \\
  H^{1}(Y) \arrow[r, "a(\gamma^{n+m-1}(\mathfrak{z}))"'] & H^{2n-1}(X)(n-1) \arrow[u, "\psi_X"']
\end{tikzcd}

\begin{tikzcd}
  H^{1}(Y, \mathbb{Q}_{\ell}) \arrow[r, "a(\gamma(Z))"] & H^{2n-1}(X, \mathbb{Q}_{\ell})(n-1) \arrow[d, "\wr"] \\
  H^{1}(A_{Y}, \mathbb{Q}_{\ell}) \arrow[u, "\wr"] \arrow[r, "u^{(1)}"] & H^{1}(B_{X}, \mathbb{Q}_{\ell})
\end{tikzcd}

\begin{tikzcd}
  H^{2n-1}(X, \mathbb{Q}_{\ell})(n-1) \arrow[r, "a(\gamma(D))"] \arrow[d, "\Psi_{X}"'] & H^{1}(Y, \mathbb{Q}_{\ell}) \\
  H^{1}(B_{X}, \mathbb{Q}_{\ell}) \arrow[r, "u_{D}^{(1)}"] & H^{1}(A_{Y}, \mathbb{Q}_{\ell}) \arrow[u, "\Phi_{Y}"']
\end{tikzcd}

\begin{tikzcd}
  H^{2n-1}(X, \mathbb{Q}_{\ell})(n-1) \arrow[r, "\Psi_{X}"] & H^{1}(B_{X}, \mathbb{Q}_{\ell}) \\
  H^{1}(X, \mathbb{Q}_{\ell}) \arrow[u, "\lambda"] & H^{1}(A_{X}, \mathbb{Q}_{\ell}) \arrow[u, "\mu"'] \arrow[l, leftrightarrow, "\varphi_{X}^{(1)}"]
\end{tikzcd}

\begin{tikzcd}
  C^{1}(A) \arrow[rr] \arrow[dr, dashed] & & \mathrm{Hom}(A, A^{*})^{\mathrm{alt}} \\
  & C^{1}(A \times A) \arrow[ur, dashed] &
\end{tikzcd}

\begin{tikzcd}[column sep=huge]
  \mathcal{VA}^{\circ} \arrow[r, "*"] \arrow[d, "(H^{1})^{\circ}"'] & \mathcal{VA} \arrow[d, "H^{1}"] \\
  \mathrm{Mod}\,\mathbb{Q}_{\ell}^{\circ} \arrow[r, "{\mathrm{Hom}(\cdot,\, \mathbb{Q}_{\ell}(-1))}"'] & \mathrm{Mod}\,\mathbb{Q}_{\ell}
\end{tikzcd}

\begin{tikzcd}[column sep=tiny, row sep=normal, nodes={font=\scriptsize}]
  C^{1}(A) \arrow[rr] \arrow[d] & & H^{2}(A) \otimes \mathbb{Q}_{\ell}(1) = H^{2}(A, \mathbb{Q}_{\ell}(1)) = \bigwedge^{2} H^{1}(A) \otimes \mathbb{Q}_{\ell}(1) \arrow[d, "\text{dualité}"] & \\
  \mathrm{Hom}(A, A^{*}) \arrow[rr] \arrow[dr, "\text{graphe}"'] & & \mathrm{Hom}(H^{1}(A^{*}), H^{1}(A)) \arrow[dr] & \\
  & C^{n}(A \times A^{*}) \arrow[rr] & & H^{2n}(A \times A^{*}) \otimes \mathbb{Q}_{\ell}(n)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
  & & A_{\mathrm{num}} & \\
  & & A_{\tau} \arrow[u, "\overset{?}{\simeq}"'] \arrow[r, "\overset{?}{\simeq}"] & A_{\mathbb{Q}_{\ell}\text{-hom}} \\
  & & A_{\mathrm{alg}} \arrow[u] \arrow[r, "\overset{?}{\simeq}"] & A_{\mathbb{Z}_{\ell}\text{-hom}} \arrow[u] \\
  & & A_{\mathrm{pic}} \arrow[u] & \\
  G_{\mathrm{top}}K \arrow[uuurr] \arrow[uurrr, dashed, "?"'] & & A_{\mathrm{alb}} \arrow[u, "\simeq ?"'] & \\
  G_{\mathrm{alg}}K \arrow[u] & & A_{\mathrm{lin}} \arrow[u, "\simeq ?"'] \arrow[ull, "\text{surj}"'] & \\
  & CK \arrow[ul, "\text{surj}"] \arrow[ur] & &
\end{tikzcd}

\begin{tikzcd}[column sep=huge]
A \arrow[r, "\text{hom. surjectif}"] & \mathcal{A}_{0}(A)^{\tau} \arrow[l, bend left=40, "\text{(hom. injectif)}"]
\end{tikzcd}

\begin{tikzcd}
{[2, 2\,\mathrm{bis}, 3, 3\,\mathrm{bis}]} \arrow[r, leftrightarrow] & {[4, 4\,\mathrm{bis}]} \arrow[r, Rightarrow] & {[5]} \\
{[6, 6\,\mathrm{bis}]} \arrow[u, Rightarrow] & & \\
5^{\circ} \arrow[u, Rightarrow] & &
\end{tikzcd}

\begin{tikzcd}[column sep=large]
 & C \times S & \\
C \arrow[d, hook, "\operatorname{codim} j+1"'] & P(N) \arrow[l] \arrow[u, no head, "\simeq" description] \arrow[d, hook, "\alpha"] & C_{y} \arrow[l, hook'] \arrow[d, hook, "\alpha_{y}"] \\
X & X' \arrow[l, "f"] \arrow[d] & Y(y) \arrow[l, hook', "i'_{y}"] \arrow[d] \arrow[ll, bend left=35, "i_{y}"] \\
 & S & y \arrow[l]
\end{tikzcd}