298 lines
11 KiB
Plaintext
298 lines
11 KiB
Plaintext
\documentclass[crop,tikz]{standalone}
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\input{common-headers}
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\input{sigles}
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\begin{document}
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%1
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\begin{tikzpicture}
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\node (A) at (0,0) {$\cat{A}$};
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\node (B) at (4,0) {$\cat{B}$};
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\node (C) at (2,0) {$\cat{C}$};
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\draw[-Stealth] (A) to node[auto] {$S$} (C);
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\draw[-Stealth] (B) to node[auto,swap] {$T$} (C);
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\end{tikzpicture}
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%2
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\begin{tikzpicture}
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\node (sa1) at (0,2) {$S(\alpha)$};
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\node (sa2) at (2,2) {$S(\alpha')$};
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\node (tb2) at (2,0) {$T(\beta')$};
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\node (tb1) at (0,0) {$T(\beta)$};
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\draw[-Stealth] (sa1) to node[auto] {$S(g)$} (sa2);
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\draw[-Stealth] (sa1) to node[auto,swap] {$f$} (tb1);
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\draw[-Stealth] (sa2) to node[auto] {$f'$} (tb2);
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\draw[-Stealth] (tb1) to node[auto,swap] {$T(h)$} (tb2);
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\end{tikzpicture}
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%3
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\begin{tikzpicture}
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\node (M0) at (2,0) {$M_0$};
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\node (M1) at (1,2) {$M$};
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\node (M2) at (3,2) {$M'$};
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\draw[-Stealth] (M1) to node[auto,swap] {$v_{M}$} (M0);
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\draw[-Stealth] (M2) to node[auto] {$v_{M'}$} (M0);
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\draw[-Stealth] (M1) to node[auto] {$a$} (M2);
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\end{tikzpicture}
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%4: Produit
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\begin{tikzpicture}[node distance=1cm and 2cm]
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\node (P) at (0,0) {$P$};
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\node (X) [left=of P] {$X$};
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\node (Y) [right=of P] {$Y$};
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\node (Q) [above=of P] {$Q$};
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\draw[-Stealth] (P) to node[auto] {$p_1$} (X);
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\draw[-Stealth] (P) to node[auto,swap] {$p_2$} (Y);
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\draw[-Stealth] (Q) to node[auto,swap] {$p'_1$} (X);
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\draw[-Stealth] (Q) to node[auto] {$p'_2$} (Y);
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\draw[-Stealth,dashed] (Q) to node[auto] {$\exists ! u$} (P);
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\end{tikzpicture}
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%5 Coproduit
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\begin{tikzpicture}[node distance=1cm and 2cm]
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\node (P) at (0,0) {$P$};
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\node (X) [left=of P] {$X$};
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\node (Y) [right=of P] {$Y$};
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\node (Q) [above=of P] {$Q$};
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\draw[-Stealth] (X) to node[auto,swap] {$i_1$} (P);
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\draw[-Stealth] (Y) to node[auto] {$i_2$} (P);
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\draw[-Stealth] (X) to node[auto] {$i'_1$} (Q);
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\draw[-Stealth] (Y) to node[auto,swap] {$i'_2$} (Q);
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\draw[-Stealth,dashed] (P) to node[auto,swap] {$\exists ! u$} (Q);
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\end{tikzpicture}
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%6 Produit fibré (1) aka Pullback
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\begin{tikzpicture}
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\node (X) at ( 0,0) {$X$};
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\node (Y) at ( 2,2) {$Y$};
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\node (Z) at ( 2,0) {$Z$};
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\node (P) at ( 0,2) {$P$};
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\draw[-Stealth] (X) to node[auto,swap] {$f$} (Z);
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\draw[-Stealth] (Y) to node[auto] {$g$} (Z);
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\draw[-Stealth] (P) to node[auto,swap] {$p_1$} (X);
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\draw[-Stealth] (P) to node[auto] {$p_2$} (Y);
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\end{tikzpicture}
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%7 Produit fibré (2) Pullback
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\begin{tikzpicture}
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\node (X) at ( 0,0) {$X$};
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\node (Y) at ( 2,2) {$Y$};
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\node (Z) at ( 2,0) {$Z$};
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\node (P) at ( 0,2) {$P$};
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\node (Q) at (-1,3) {$Q$};
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\draw[-Stealth] (X) to node[auto,swap] {$f$} (Z);
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\draw[-Stealth] (Y) to node[auto] {$g$} (Z);
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\draw[-Stealth] (P) to node[auto,swap] {$p_1$} (X);
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\draw[-Stealth] (P) to node[auto] {$p_2$} (Y);
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\draw[-Stealth,bend right] (Q) to node[auto,swap] {$p'_1$} (X);
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\draw[-Stealth,bend left] (Q) to node[auto] {$p'_2$} (Y);
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\draw[-Stealth,dashed] (Q) to node[auto] {$\exists ! u$} (P);
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\end{tikzpicture}
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%8 Somme amalgamée (1) aka Pushout
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\begin{tikzpicture}
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\node (X) at ( 0,0) {$X$};
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\node (Y) at ( 2,2) {$Y$};
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\node (Z) at ( 2,0) {$Z$};
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\node (P) at ( 0,2) {$P$};
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\draw[-Stealth] (Z) to node[auto] {$f$} (X);
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\draw[-Stealth] (Z) to node[auto,swap] {$g$} (Y);
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\draw[-Stealth] (X) to node[auto] {$i_1$} (P);
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\draw[-Stealth] (Y) to node[auto,swap] {$i_2$} (P);
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\end{tikzpicture}
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%9 Somme amalgamée (2) aka Pushout
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\begin{tikzpicture}
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\node (X) at ( 0,0) {$X$};
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\node (Y) at ( 2,2) {$Y$};
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\node (Z) at ( 2,0) {$Z$};
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\node (P) at ( 0,2) {$P$};
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\node (Q) at (-1,3) {$Q$};
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\draw[-Stealth] (Z) to node[auto] {$f$} (X);
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\draw[-Stealth] (Z) to node[auto,swap] {$g$} (Y);
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\draw[-Stealth] (X) to node[auto] {$i_1$} (P);
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\draw[-Stealth] (Y) to node[auto,swap] {$i_2$} (P);
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\draw[-Stealth,bend left] (X) to node[auto] {$i'_1$} (Q);
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\draw[-Stealth,bend right] (Y) to node[auto,swap] {$i'_2$} (Q);
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\draw[-Stealth,dashed] (P) to node[auto,swap] {$\exists ! u$} (Q);
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\end{tikzpicture}
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%10 Slice catégorie
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\begin{tikzpicture}[node distance=1.2cm and 1cm]
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\node (X) at (0,0) {$X$};
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\node (Y1) [above left =of X] {$Y1$};
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\node (Y2) [above right=of X] {$Y2$};
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\draw[-Stealth] (Y1) to node[auto] {$g$} (Y2);
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\draw[-Stealth] (Y1) to node[auto,swap] {$f_1$} (X);
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\draw[-Stealth] (Y2) to node[auto] {$f_2$} (X);
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\end{tikzpicture}
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%11
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\begin{tikzpicture}
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\node (M1) at (-5,0) {$\model{M}{1}$};
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\node (M12) at (-3,0) {$\model{M}{12}$};
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\node (M2) at (-1,0) {$\model{M}{2}$};
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\node (M) at (-3,2) {$\modelM'$};
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\node (equiv) at (0,0) {$\Leftrightarrow$};
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\node (E1) at (1,0) {$E_{\model{M}{1}}$};
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\node (E12) at (3,0) {$E_{\model{M}{12}}$};
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\node (E2) at (5,0) {$E_{\model{M}{2}}$};
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\node (ER) at (3,-2) {$E_{\model{M}{S}}$};
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\node (EM) at (3,2) {$E_{\modelM'}$};
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\draw[-Stealth] (M12) to node[auto,swap] {$\absA_1$} (M1);
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\draw[-Stealth] (M12) to node[auto] {$\absA_2$} (M2);
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\draw[-Stealth,dashed] (M) to node[auto] {$\absA'$} (M12);
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\draw[-Stealth] (M) to node[auto,swap] {$\absA'_1$} (M1);
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\draw[-Stealth] (M) to node[auto] {$\absA'_2$} (M2);
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\draw[-Stealth] (E1) to node[auto] {$f_{\absA_1}$} (E12);
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\draw[-Stealth] (E2) to node[auto,swap] {$f_{\absA_2}$} (E12);
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\draw[-Stealth,dashed] (E12) to node[auto,swap] {$f_{\absA'}$} (EM);
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\draw[-Stealth] (E1) to node[auto] {$f_{\absA'_1}$} (EM);
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\draw[-Stealth] (E2) to node[auto,swap] {$f_{\absA'_2}$} (EM);
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\draw[-Stealth] (ER) to node[auto] {$\sigma_{\model{M}{1}}$} (E1);
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\draw[-Stealth] (ER) to node[auto,swap] {$\sigma_{\model{M}{2}}$} (E2);
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\end{tikzpicture}
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%12
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\begin{tikzpicture}
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\node (M1) at (-5,0) {$\model{M}{1}$};
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\node (M12) at (-3,2) {$\model{M}{12}^0$};
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\node (M2) at (-1,0) {$\model{M}{2}$};
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\node (M0) at (-3,0) {$\modelM_0$};
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\node (equiv) at (0,0) {$\Leftrightarrow$};
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\node (E1) at (1,0) {$E_{\model{M}{1}}$};
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\node (E12) at (3,2) {$E_{\model{M}{12}^0}$};
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\node (E2) at (5,0) {$E_{\model{M}{2}}$};
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\node (ER) at (3,-2) {$E_{\model{M}{S}}$};
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\node (EM) at (3,0) {$E_{\modelM_0}$};
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\draw[-Stealth] (M12) to node[auto,swap] {$\absA_1$} (M1);
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\draw[-Stealth] (M12) to node[auto] {$\absA_2$} (M2);
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\draw[-Stealth] (M1) to node[auto] {$\absA^0_1$} (M0);
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\draw[-Stealth] (M2) to node[auto,swap] {$\absA^0_2$} (M0);
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\draw[-Stealth] (E1) to node[auto] {$f_{\absA_1}$} (E12);
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\draw[-Stealth] (E2) to node[auto,swap] {$f_{\absA_2}$} (E12);
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\draw[-Stealth] (EM) to node[auto,swap] {$f_{\absA^0_1}$} (E1);
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\draw[-Stealth] (EM) to node[auto] {$f_{\absA^0_2}$} (E2);
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\draw[-Stealth] (ER) to node[auto] {$\sigma_{\model{M}{1}}$} (E1);
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\draw[-Stealth] (ER) to node[auto,swap] {$\sigma_{\model{M}{2}}$} (E2);
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\draw[-Stealth] (ER) to node[auto,swap] {$\sigma_{\model{M}{0}}$} (EM);
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\end{tikzpicture}
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%13
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\begin{tikzpicture}
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\node (Mp) at (-3,1) {$\model{M}{+}$};
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\node (Mm) at (-1,1) {$\model{M}{-}$};
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\node (eq) at (0,1) {$\Leftrightarrow$};
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\node (Er) at (2,0) {$E_{\model{M}{S}}$};
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\node (Ep) at (1,2) {$E_{\model{M}{+}}$};
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\node (Em) at (3,2) {$E_{\model{M}{-}}$};
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\draw[-Stealth] (Mp) to node[auto] {$\absA$} (Mm);
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\draw[-Stealth] (Er) to node[auto] {$\sigma_{\model{M}{+}}$} (Ep);
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\draw[-Stealth] (Er) to node[auto,swap] {$\sigma_{\model{M}{-}}$} (Em);
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\draw[-Stealth] (Em) to node[auto,swap] {$f_{\absA}$} (Ep);
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\end{tikzpicture}
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%14
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\begin{tikzpicture}
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\node (Mp) at (-3,2) {$\model{M}{+}$};
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\node (Mm) at (-1,2) {$\model{M}{-}$};
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\node (eq) at (0,2) {$\Leftrightarrow$};
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\node (Er) at (2,0) {$E_{\model{M}{S}}$};
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\node (Ep) at (1,2) {$E_{\model{M}{+}}$};
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\node (Em) at (3,2) {$E_{\model{M}{-}}$};
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\node (eq) at (4,2) {$\stackrel{\ftr{U}_{\cat{AMon}}}\mapsfrom$};
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\node (ap) at (5,2) {$\Phi_+$};
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\node (am) at (7,2) {$\Phi_-$};
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\draw[-Stealth] (Mp) to node[auto] {$\absA$} (Mm);
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\draw[-Stealth] (Er) to node[auto] {$\sigma_{\model{M}{+}}$} (Ep);
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\draw[-Stealth] (Er) to node[auto,swap] {$\sigma_{\model{M}{-}}$} (Em);
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\draw[-Stealth] (Em) to node[auto,swap] {$f_{\absA}$} (Ep);
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\draw[-Stealth] (am) to node[auto,swap] {$h$} (ap);
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\end{tikzpicture}
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%15
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\begin{tikzpicture}
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\node (M1) at (-2,0) {$\model{M}{1}$};
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\node (M12) at (0,0) {$\model{M}{12}$};
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\node (M2) at (2,0) {$\model{M}{2}$};
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\node (M) at (0,2) {$\modelM'$};
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\draw[-Stealth] (M1) to node[auto] {$\absA_1$} (M12);
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\draw[-Stealth] (M2) to node[auto,swap] {$\absA_2$} (M12);
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\draw[-Stealth,dashed] (M12) to node[auto,swap] {$\absA'$} (M);
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\draw[-Stealth] (M1) to node[auto] {$\absA'_1$} (M);
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\draw[-Stealth] (M2) to node[auto,swap] {$\absA'_2$} (M);
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\end{tikzpicture}
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%16
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\begin{tikzpicture}
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\node (M1) at (-2,0) {$E_{\model{M}{1}}$};
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\node (M12) at (0,0) {$E_{\model{M}{12}}$};
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\node (M2) at (2,0) {$E_{\model{M}{2}}$};
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\node (M) at (0,2) {$E_{\modelM'}$};
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\node (R) at (0,-2) {$E_{\model{M}{S}}$};
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\draw[-Stealth] (M12) to node[auto,swap] {$f_{\absA_1}$} (M1);
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\draw[-Stealth] (M12) to node[auto] {$f_{\absA_2}$} (M2);
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\draw[-Stealth,dashed] (R) to node[auto,swap] {$\sigma_{\model{M}{12}}$} (M12);
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\draw[-Stealth] (R) to node[auto] {$\sigma_{\model{M}{1}}$} (M1);
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\draw[-Stealth] (R) to node[auto,swap] {$\sigma_{\model{M}{2}}$} (M2);
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\draw[-Stealth] (M) to node[auto,swap] {$f_{\absA'_1}$} (M1);
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\draw[-Stealth] (M) to node[auto] {$f_{\absA'_2}$} (M2);
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\draw[-Stealth,dashed] (M) to node[auto] {$f_{\absA'}$} (M12);
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\end{tikzpicture}
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%17
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\begin{tikzpicture}
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\node (M1) at (-5,0) {$\model{M}{1}$};
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\node (M12) at (-3,0) {$\model{M}{12}^0$};
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\node (M2) at (-1,0) {$\model{M}{2}$};
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\node (M0) at (-3,2) {$\model{M}{0}$};
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\node (equiv) at (0,0) {$\Leftrightarrow$};
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\node (E1) at (1,0) {$E_{\model{M}{1}}$};
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\node (E12) at (3,0) {$E_{\model{M}{12}^0}$};
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\node (E2) at (5,0) {$E_{\model{M}{2}}$};
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\node (ER) at (3,-2) {$E_{\model{M}{S}}$};
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\node (EM) at (3,2) {$E_{\model{M}{0}}$};
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\draw[-Stealth] (M1) to node[auto] {$\absA_1$} (M12);
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\draw[-Stealth] (M2) to node[auto,swap] {$\absA_2$} (M12);
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%%\draw[-Stealth,dashed] (M0) to node[auto] {$\absA'$} (M12);
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\draw[-Stealth] (M0) to node[auto,swap] {$\absA^0_1$} (M1);
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\draw[-Stealth] (M0) to node[auto] {$\absA^0_2$} (M2);
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\draw[-Stealth] (E12) to node[auto,swap] {$f_{\absA_1}$} (E1);
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\draw[-Stealth] (E12) to node[auto] {$f_{\absA_2}$} (E2);
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%\draw[-Stealth,dashed] (E12) to node[auto,swap] {$f_{\absA'}$} (EM);
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\draw[-Stealth] (E1) to node[auto] {$f_{\absA^0_1}$} (EM);
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\draw[-Stealth] (E2) to node[auto,swap] {$f_{\absA^0_2}$} (EM);
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\draw[-Stealth] (ER) to node[auto] {$\sigma_{\model{M}{1}}$} (E1);
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\draw[-Stealth] (ER) to node[auto,swap] {$\sigma_{\model{M}{2}}$} (E2);
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\draw[-Stealth,dashed] (ER) to node[auto,swap] {$\sigma_{\model{M}{12}^0}$} (E12);
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\end{tikzpicture}
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\end{document}
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