Cote n° 156-7 · pages 15–107
· 13 commutative diagrams · [Chapitre] VII. Analysis situs (troisième mouture) : notes manuscrites (23-26/06/1986).
Inventory dating : 1986
Édition de démonstration
LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& & \mathrm{Omb}\, H \arrow[dl, no head] \arrow[dr, no head] & & \\
& \mathrm{Omb}\, F \arrow[dl, no head] \arrow[dr, no head] & & \mathrm{Omb}\, G \arrow[dl, no head] \arrow[dr, no head] & \\
\mathrm{Omb}\, F' \arrow[dr, no head] & & \mathrm{Omb}\, L \arrow[dl, no head] \arrow[dr, no head] & & \mathrm{Omb}\, G' \arrow[dl, no head] \\
& \mathrm{Omb}\, F'_{L} & & \mathrm{Omb}\, G'_{L} &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& & \widetilde{H} & & \\
& \widetilde{F} \arrow[ur, hook] & & \widetilde{G} \arrow[ul, hook'] & \\
& & \widetilde{L} \arrow[ul, hook'] \arrow[ur, hook] & & \widetilde{G}' \arrow[ul] \\
\widetilde{F}' \arrow[uur] & & & & \\
& \widetilde{F}'_{L} \arrow[ul, hook'] \arrow[uur] & & \widetilde{G}'_{L} \arrow[uul] \arrow[uur, hook] &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small]
\mathrm{Omb}\, F \arrow[dr, hook] & & \mathrm{Omb}\, G \arrow[dl, hook'] \\
& \mathrm{Omb}(F) \cap \mathrm{Omb}(G) \arrow[d, hook] & \\
& \mathrm{Omb}(L) &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& Z \arrow[r, no head, "\ll" description] & X \\
& Z' \arrow[u, no head, "\leq" description] \arrow[r, no head, "\ll" description] & X' \arrow[u, no head, "\leq" description] \\
x \arrow[ur, no head, "\ll" description] & &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
\mathrm{omb}(X) \arrow[dr, no head] & & \mathrm{omb}(Y) \arrow[dl, no head] \\
& \mathrm{omb}(X) \cap \mathrm{omb}(Y) \arrow[d, no head] & \\
& \mathrm{omb}(L) &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& Z & \\
X \arrow[ur, no head, "\leq" description] & & Y \arrow[ul, no head, "\leq" description] \\
& L \arrow[ul, no head, "\leq" description] \arrow[ur, no head, "\leq" description] &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
X' \arrow[r, no head, "\leq" description] & X \\
x \arrow[u, no head, "\ll" description] \arrow[r, no head, "\ll" description] & Z \arrow[u, no head, "\leq" description]
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
X' \arrow[r, no head, "\leq" description] & X & \\
S \arrow[u, no head, "\leq" description] \arrow[r, no head, "\leq" description] & Z \arrow[u, no head, "\leq" description] \arrow[r, no head, "\leq" description] & Y \\
x \arrow[u, no head, "\ll" description] & &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
S \arrow[r, no head, "\leq" description] & Y \\
x \arrow[u, no head, "\ll" description] \arrow[r, no head, "\ll" description] & Y' \arrow[u, no head, "\leq" description]
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& Z \arrow[r, no head, "\ll" description] & X \\
x \arrow[r, no head, "\ll" description] & Z' \arrow[u, no head, "\leq" description] \arrow[r, no head, "\ll" description] & X' \arrow[u, no head, "\leq" description]
\end{tikzcd}LaTeX source
\begin{tikzcd}
Y' \arrow[r, no head, "\ll" description] & Y \arrow[r, no head, "\overset{\circ}{\ll}" description] \arrow[d, no head, "\geq" description] & X \arrow[d, no head, "\geq" description] \\
& Y_{\partial X} \arrow[r, no head, "\ll" description] \arrow[d, no head, "\geq" description] & \partial X \\
& \partial Y &
\end{tikzcd}LaTeX source
\begin{tikzcd}[column sep=small, row sep=small]
& \widetilde{X} \arrow[dl, no head] \arrow[dr, no head] & & \widetilde{Y} \arrow[dl, no head] \arrow[dr, no head] & \\
\widetilde{X}' \arrow[dr, no head] & & L \arrow[dl, no head] \arrow[dr, no head] & & \widetilde{Y}' \arrow[dl, no head] \\
& X'_L \arrow[dr, no head] & & Y'_L \arrow[dl, no head] & \\
& & L' & &
\end{tikzcd}LaTeX source
\begin{tikzcd}[row sep=small]
\between\text{-magasins satisfaisant At L1, L2, L3 et At C (spéc.)} \arrow[d, Rightarrow] \\
\mathrel{|{\circ}|}\text{-magasins satisfaisant } (***) \text{ (compatibilisme)}
\end{tikzcd}