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1 \documentclass{jarticle}
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2 \usepackage[dvipdfm]{graphicx}
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3 \usepackage{tikz}
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4 \usepackage{tikz-cd}
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5 \usetikzlibrary{matrix,arrows,decorations.pathmorphing}
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6 \usetikzlibrary{positioning}
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7 \usepackage{amsmath}
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8
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9 \begin{document}
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10
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11 \date{}
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12 \title{{\bf Commutative Diagram Exmamples}}
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13 \author{}
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14
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15 The tikz package
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16 This is a general purpose graphics package. To load it for this document, I used:
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17
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18
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19
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20 \begin{tikzcd}
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21 A \arrow{r}{a} \arrow{d}{b}
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22 &B \arrow{d}{c}\\
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23 C \arrow{r}{d} &D
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24 \end{tikzcd}
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25
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26
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27 \begin{tikzpicture}[scale=1.5]
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28 \node (A) at (0,1) {$A$};
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29 \node (B) at (1,1) {$B$};
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30 \node (C) at (0,0) {$C$};
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31 \node (D) at (1,0) {$D$};
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32 \path[->,font=\scriptsize,>=angle 90]
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33 (A) edge node[above]{$a$} (B)
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34 (A) edge node[right]{$b$} (C)
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35 (B) edge node[right]{$c$} (D)
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36 (C) edge node[above]{$d$} (D);
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37 \end{tikzpicture}
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38
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39
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40 This is part of: Guide to Commutative Diagrams, www.jmilne.org/not/CDGuide.html Last revised October 30, 2012
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41
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42 \begin{tikzcd}
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43 ABC A \arrow[hook]{r}\arrow[two heads]{rd}
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44 &B \arrow[dotted]{d}\arrow[hookleftarrow]{r}
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45 &C \arrow[two heads]{ld}\\ D &D
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46 \end{tikzcd}
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47
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48
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49 \begin{tikzcd}
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50 A \arrow[hook]{r}{u}[swap]{b}
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51 Aub Bub C \arrow[two heads]{rd}{u}[swap]{b}
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52 &B \arrow[dotted]{d}{r}[swap]{l}
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53 \arrow[hookleftarrow]{r}{u}[swap]{b}
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54 D &C \arrow[two heads]{ld}{b}[swap]{u}\\ &D
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55 \end{tikzcd}
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56
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57 \begin{tikzcd}
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58 A\arrow{r}\arrow{d}
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59 &B\arrow{r}{\text{very long label}}\arrow{d}
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60 &C\arrow{d}\\
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61 DEF D\arrow{r}&E\arrow{r}&F
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62 \end{tikzcd}
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63
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64 % \begin{tikzcd}[column sep=large]
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65 % A\arrow{r}\arrow{d}
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66
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67
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68 \begin{tikzcd}
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69 A B A\arrow[bend left]{r}\arrow[bend right]{r}&B
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70 \end{tikzcd}
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71
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72
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73 \begin{tikzcd}
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74 T\arrow[bend left]{drr}{x}
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75 \arrow[bend right]{ddr}[swap]{y}
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76 \arrow[dotted]{dr}[description]{(x,y)} & & \\
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77 & X \times_Z Y \arrow{r}{p} \arrow{d}{q} & X \arrow{d}{f} \\
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78 & Y \arrow{r}{g} & Z
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79 \end{tikzcd}
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80
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81
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82
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83
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84
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85
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86 \begin{tikzpicture}
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87 \node (A) at (-1,0) {$A$};
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88 \node (B) at (1,0) {$B$};
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89 \node at (0,0) {\rotatebox{270}{$\Rightarrow$}};
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90 \path[->,font=\scriptsize,>=angle 90]
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91 (A) edge [bend left] node[above] {$\alpha$} (B)
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92 edge [bend right] node[below] {$\beta$} (B);
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93 \end{tikzpicture}
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94
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95 \begin{tikzpicture}
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96 \node (P0) at (90:2.8cm) {$X\otimes (Y\otimes (Z\otimes T))$};
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97 \node (P1) at (90+72:2.5cm) {$X\otimes ((Y\otimes Z)\otimes T))$} ;
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98 \node (P2) at (90+2*72:2.5cm) {${(X\otimes (Y\otimes Z))}\otimes T$};
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99 \node (P3) at (90+3*72:2.5cm) {$((X\otimes Y){\otimes Z)\otimes T}$};
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100 \node (P4) at (90+4*72:2.5cm) {$(X\otimes Y)\otimes (Z\otimes T)$};
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101 \draw
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102 (P0) edge[->,>=angle 90] node[left] {$1\otimes\phi$} (P1)
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103 (P1) edge[->,>=angle 90] node[left] {$\phi$} (P2)
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104 (P2) edge[->,>=angle 90] node[above] {$\phi\otimes 1$} (P3)
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105 (P4) edge[->,>=angle 90] node[right] {$\phi$} (P3)
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106 (P0) edge[->,>=angle 90] node[right] {$\phi$} (P4);
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107 \end{tikzpicture}
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108
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109
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110 \begin{tikzpicture}
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111 \node (a) at (0,0) {$Y\times_X Y$};
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112 \node (b) at (2,0) {$Y$};
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113 \node (c) at (3.5,0) {$X$};
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114 \path[->,font=\scriptsize,>=angle 90]
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115 ([yshift= 2pt]a.east) edge node[above] {$p_1$} ([yshift= 2pt]b.west)
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116 ([yshift= -2pt]a.east) edge node[below] {$p_2$} ([yshift= -2pt]b.west)
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117 (b) edge (c);
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118 \end{tikzpicture}
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119
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120 \begin{tikzpicture}[descr/.style={fill=white},text height=1.5ex, text depth=0.25ex]
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121 \node (a) at (0,0) {$\mathsf{S}(Z)$};
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122 \node (b) at (2.5,0) {$\mathsf{S}(X)$};
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123 \node (c) at (5,0) {$\mathsf{S}(U).$};
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124 \path[->,font=\scriptsize,>=angle 90]
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125 ([yshift= 9pt]b.west) edge node[above] {$i^{\ast}$} ([yshift= 9pt]a.east)
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126 (a.east) edge node[descr] {$i_{\ast}$} (b.west)
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127 ([yshift= -9pt]b.west) edge node[below] {$i^!$} ([yshift= -9pt]a.east)
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128 ([yshift= 9pt]c.west) edge node[above] {$j_!$} ([yshift= 9pt]b.east)
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129 (b.east) edge node[descr] {$j^{\ast}$} (c.west)
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130 ([yshift= -9pt]c.west) edge node[below] {$j_*$} ([yshift= -9pt]b.east);
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131 \end{tikzpicture}
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132
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133
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134 \begin{tikzpicture}[>=angle 90,scale=2.2,text height=1.5ex, text depth=0.25ex]
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135 %%First place the nodes
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136 \node (k-1) at (0,3) {$0$};
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137 \node (k0) [right=of k-1] {$Ker f$};
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138 \node (k1) [right=of k0] {$Ker a$};
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139 \node (k2) [right=of k1] {$Ker b$};
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140 \node (k3) [right=of k2] {$Ker c$};
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141 \node (a1) [below=of k1] {$A$};
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142 \node (a2) [below=of k2] {$B$};
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143 \node (a3) [below=of k3] {$C$};
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144 \node (a4) [right=of a3] {$0$};
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145 \node (b1) [below=of a1] {$A’$};
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146 \node (b0) [left=of b1] {$0$};
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147 \node (b2) [below=of a2] {$B’$};
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148 \node (b3) [below=of a3] {$C’$};
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149 \node (c1) [below=of b1] {$Coker a$};
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150 \node (c2) [below=of b2] {$Coker b$};
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151 \node (c3) [below=of b3] {$Coker c$};
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152 \node (c4) [right=of c3] {$Coker g’$};
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153 \node (c5) [right=of c4] {$0$};
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154 %%Draw the red arrows
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155 \draw[->,red,font=\scriptsize]
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156 (k-1) edge (k0)
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157 (k0) edge (k1)
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158 (k1) edge (k2)
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159 (k2) edge (k3)
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160 (c1) edge (c2)
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161 (c2) edge (c3)
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162 (c3) edge (c4)
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163 (c4) edge (c5);
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164 %%Draw the curvy red arrow
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165 %\draw[->,red]
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166 %(k3) edge[out=0,in=180,red] node[pos=0.55,yshift=5pt] {$d$} (c1);
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167 %%Draw the black arrows
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168 %\draw[->]
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169 (k1) edge (a1)
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170 (k2) edge (a2)
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171 (k3) edge (a3)
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172 (b1) edge (c1)
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173 (b2) edge (c2)
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174 (b3) edge (c3);
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175 %%Draw the thick blue arrows
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176 \draw[->,font=\scriptsize,blue,thick]
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177 (a1) edge node[auto] {$f$} (a2)
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178 (a2) edge node[auto] {$g$} (a3)
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179 (a3) edge (a4)
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180 (a1) edge node[auto] {$a$} (b1)
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181 (a2) edge node[auto] {$b$} (b2)
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182 (a3) edge node[auto] {$c$} (b3)
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183 (b0) edge (b1)
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184 (b1) edge node[below] {$f’$} (b2)
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185 (b2) edge node[below] {$g’$} (b3);
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186 \end{tikzpicture}
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187
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188
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189 \end{document}
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