Cote n° 117 · pages 7–24
· 12 diagrammes commutatifs · Théories homotopiques : notes manuscrites (1983, s.d.).
Datation de l’inventaire : 1983
Édition de démonstration
LaTeX source
\begin{tikzcd}
\mathcal H(B) \arrow[r, "\mathcal H(f)"] \arrow[d, "\alpha_B"'] & \mathcal H(A) \arrow[d, "\alpha_A"] \\
\underline{\mathrm{Hom}}(B, \mathrm{Hot}_{\mathcal H}) \arrow[r, "f^{*}_{\mathrm{Hot}_{\mathcal H}}"'] & \underline{\mathrm{Hom}}(A, \mathrm{Hot}_{\mathcal H})
\end{tikzcd}LaTeX source
\begin{tikzcd}
\mathcal H(A) \arrow[r, "\underline{L}_A"] \arrow[d, "f_!"'] & \mathcal H(\widehat{A}) \arrow[d, "(f^{*}_{\wedge})^{*}_{\mathcal H} \overset{\mathrm{def}}{=} \hat f_!"] \\
\mathcal H(B) \arrow[r, "\underline{L}_B"'] & \mathcal H(B^{\wedge})
\end{tikzcd}LaTeX source
\begin{tikzcd}
A^{\circ\wedge} \times \mathcal T \arrow[d, "f^{\circ}_{\mathrm{top}} \times \mathrm{id}_{\mathcal T}"] \\
B^{\circ\wedge} \times \mathcal T
\end{tikzcd}LaTeX source
\begin{tikzcd}
A \arrow[r, "g'"] \arrow[d, "f"'] & A' \arrow[d, "f'"] \\
B \arrow[r, "g"'] & B'
\end{tikzcd}LaTeX source
\begin{tikzcd}
A_0 \arrow[r, "i"] \arrow[d, "p_0"'] & A \arrow[dl, no head, "p"] \\
\Delta_0 &
\end{tikzcd}LaTeX source
\begin{tikzcd}
\mathcal{H}(A) \arrow[r, "(h_A)^{\mathcal{H}}_{!}"] \arrow[d, "j^{\mathcal{H}}_{!}"'] & \mathcal{H}(A^{\wedge}) \arrow[d, "(j^{*}_{\wedge})^{*}_{\mathcal{H}}"] \\
\mathcal{H}(B) \arrow[r, "(h_B)^{\mathcal{H}}_{!}"'] & \mathcal{H}(B^{\wedge})
\end{tikzcd}LaTeX source
\begin{tikzcd}
\bullet & \\
c \arrow[u, "A'"] \arrow[r, "A''"'] & \bullet
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& e \arrow[d] & \Omega Z \arrow[l] \arrow[d] \\
e \arrow[d] & \Omega Y \arrow[l] \arrow[d] & \Omega X \arrow[l] \arrow[d] \\
X \arrow[d] & Z \arrow[l] \arrow[d] & e \arrow[l] \\
Y & e \arrow[l] &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& & & & e \arrow[d] & \Omega^{3} Z \arrow[l] \arrow[d, "\Omega^{3} g"] & \Omega^{4} Y \arrow[l, "\Omega^{3} h"'] \arrow[d] \\
& & & e \arrow[d] & \Omega^{3} Y \arrow[l] \arrow[d, "\Omega^{2} h"] & \Omega^{3} X \arrow[l, "\Omega^{3} f"'] \arrow[d] & e \arrow[l] \\
& & e \arrow[d] & \Omega^{2} X \arrow[l] \arrow[d, "\Omega^{2} f"] & \Omega^{2} Z \arrow[l, "\Omega^{2} g"'] \arrow[d] & e \arrow[l] & \\
& e \arrow[d] & \Omega Z \arrow[l] \arrow[d, "\Omega g"] & \Omega^{2} Y \arrow[l, "\Omega h"'] \arrow[d] & e \arrow[l] & & \\
e \arrow[d] & \Omega Y \arrow[l] \arrow[d, "h"] & \Omega X \arrow[l, "\Omega f"'] \arrow[d] & e \arrow[l] & & & \\
X \arrow[d, "f"'] & Z \arrow[l, "g"] \arrow[d] & e \arrow[l] & & & & \\
Y & e \arrow[l] & & & & &
\end{tikzcd}LaTeX source
\begin{tikzcd}
& P \arrow[d, no head] \\
P & Q \arrow[l]
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
& & e \arrow[dl] & & e \arrow[dl] & & e \arrow[dl] & & e \arrow[dl] & & \\
Y & X \arrow[l] & Z \arrow[l] \arrow[dl] & \Omega Y \arrow[l] \arrow[ul] & \Omega X \arrow[l] \arrow[dl] & \Omega Z \arrow[l] \arrow[ul] & \Omega^{2} Y \arrow[l] \arrow[dl] & \Omega^{2} X \arrow[l] \arrow[ul] & \Omega^{2} Z \arrow[l] \arrow[dl] & \Omega^{3} Y \arrow[l] \arrow[ul] & \cdots \arrow[l] \\
& e \arrow[ul] & & e \arrow[ul] & & e \arrow[ul] & & e \arrow[ul] & & &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
e \arrow[d] & \cdot \arrow[l, dashed] \arrow[dd, dashed, no head] & \bullet \arrow[l, dashed, no head] \arrow[d, dashed, no head] \\
X \arrow[d] & & e \arrow[ll] \arrow[dl] \\
Y & e \arrow[l] &
\end{tikzcd}