Cote n° 156-5, pages 24–41 — 13 diagrammes commutatifs

Cote n° 156-5 · pages 24–41 · 13 diagrammes commutatifs · [Chapitre] V. Algèbre des figures : notes manuscrites (14/06/1986).
Datation de l’inventaire : 1986
Édition de démonstration

batch 2 · p. 24 — lire la page1 / 13

LaTeX source

\begin{tikzcd}
S\ (= |F|) \arrow[r, hook, "i"] \arrow[d, "p\ \text{surj}"'] & T\ (= |G|) \arrow[r, hook] \arrow[d, "q\ \text{surj}"] & \mathcal{L} \\
I\ (= F) \arrow[r, "\varphi"] & J\ (= G) &
\end{tikzcd}

batch 2 · p. 25 — lire la page2 / 13

LaTeX source

\begin{tikzcd}
S \arrow[r, hook] \arrow[d, "p\ \text{surj}"] & \mathcal{L} \\
I \arrow[d, "\varphi\ \text{surj.}"] & \\
J &
\end{tikzcd}

batch 2 · p. 27 — lire la page3 / 13

LaTeX source

\begin{tikzcd}
 & S \arrow[rr, hook] \arrow[dd, "\varphi\ \text{surj}"] & & \mathcal{L} \\
 & & S' \arrow[ur, hook] \arrow[d, "\varphi'\ \text{surj}"] & \\
 & I & I' &
\end{tikzcd}

batch 2 · p. 27 — lire la page4 / 13

LaTeX source

\begin{tikzcd}
 & S \arrow[rr, hook] \arrow[dd, "\varphi"] & & \mathcal{L} \\
S \cap T \arrow[ur, hook] \arrow[rr, hook] \arrow[dd, "\psi"'] & & T \arrow[ur, hook] \arrow[dd, "\varphi'"] & \\
 & I & & \\
K \arrow[ur] \arrow[rr] & & I' &
\end{tikzcd}

batch 2 · p. 33 — lire la page5 / 13

LaTeX source

\begin{tikzcd}
I' \arrow[r, no head, "\supset" description] \arrow[d, "\varphi\ \text{surj}"'] & J' = \varphi^{-1}(J) \arrow[d] \\
I \arrow[r, no head, "\supset" description] & J \text{ partie f.}
\end{tikzcd}

batch 2 · p. 33 — lire la page6 / 13

LaTeX source

\begin{tikzcd}
I'^{*} \arrow[d, "\varphi^{*} = \varphi \mid I'^{*}"] \\
I^{*}
\end{tikzcd}

batch 2 · p. 33 — lire la page7 / 13

LaTeX source

\begin{tikzcd}
U \arrow[r, "p'"] \arrow[rr, bend right=30, "p"'] & I'^{*} \arrow[r, "\varphi^{*}"] & I^{*}
\end{tikzcd}

batch 2 · p. 33 — lire la page8 / 13

LaTeX source

\begin{tikzcd}
S \arrow[r] \arrow[rr, bend left=30, "\varphi"] & I'' \arrow[r, "\varphi''"] & I \\
T \arrow[u, hook] \arrow[r] & J'' \arrow[u, hook] \arrow[r] & J \arrow[u, hook]
\end{tikzcd}

batch 2 · p. 34 — lire la page9 / 13

LaTeX source

\begin{tikzcd}
f^{-1}(J) = T \arrow[r, hook] \arrow[d, "g_{J}"] \arrow[dd, bend right=40, "f_{J} = f \mid T"'] & S \arrow[dd, "f\ \text{surj}"] \\
J' \arrow[d, "h_{J}"] & \\
J \arrow[r, hook, "i"] & I
\end{tikzcd}

batch 2 · p. 34 — lire la page10 / 13

LaTeX source

\begin{tikzcd}
T \arrow[r, hook] \arrow[d, "g_{J}"] \arrow[dd, bend right=40, "f_{J}"'] & S \arrow[d, "g"] \\
J' \arrow[r, hook, "i'"] \arrow[d, "h_{J}"] & I' \arrow[d, "h"] \\
J \arrow[r, hook, "i"] & I
\end{tikzcd}

batch 2 · p. 35 — lire la page11 / 13

LaTeX source

\begin{tikzcd}
J' \arrow[r, hook, "i"] \arrow[d, "h_{J}"'] & K \arrow[d, "h_{K}"] \\
J \arrow[r, hook, "i"] & I
\end{tikzcd}

batch 2 · p. 36 — lire la page12 / 13

LaTeX source

\begin{tikzcd}
J' \arrow[r, "i'"] \arrow[d, "h_{J}"'] & I' \arrow[d, "h"] \\
J \arrow[r] & I
\end{tikzcd}

batch 3 · p. 41 — lire la page13 / 13

LaTeX source

\begin{tikzcd}
\varphi^{-1}(J) = J' \arrow[r, hook] \arrow[d] & I' \arrow[d, "\varphi"] & \overline{\tau}' \arrow[d] \\
J \arrow[r, hook] & I & \overline{\tau}
\end{tikzcd}