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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 There are now three ways to enter commutative diagrams using tikz: with the package tikz-cd, with matrix, and directly with tikz (listed roughly in order of decreasing ease but increasing flexibility).
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20
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21 \begin{tikzcd}
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22 A \arrow{r}{a} \arrow{d}{b}
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23 &B \arrow{d}{c}\\
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24 C \arrow{r}{d} &D
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25 \end{tikzcd}
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26
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27 \begin{tikzpicture}
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28 \matrix(m)[matrix of math nodes, row sep=2.6em, column sep=2.8em, text height=1.5ex, text depth=0.25ex]
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29 {A & B \\
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30 C & D \\ };
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31 \path[->,font=\scriptsize,>=angle 90]
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32 (m-1-1) edge node[auto] {$a$} (m-1-2)
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33 edge node[auto] {$b$} (m-2-1)
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34 (m-1-2) edge node[auto] {$c$} (m-2-2)
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35 (m-2-1) edge node[auto] {$d$} (m-2-2);
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36 \end{tikzpicture}
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37
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38 \begin{tikzpicture}[scale=1.5]
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39 \node (A) at (0,1) {$A$};
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40 \node (B) at (1,1) {$B$};
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41 \node (C) at (0,0) {$C$};
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42 \node (D) at (1,0) {$D$};
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43 \path[->,font=\scriptsize,>=angle 90]
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44 (A) edge node[above]{$a$} (B)
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45 (A) edge node[right]{$b$} (C)
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46 (B) edge node[right]{$c$} (D)
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47 (C) edge node[above]{$d$} (D);
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48 \end{tikzpicture}
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49
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50
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51 This is part of: Guide to Commutative Diagrams, www.jmilne.org/not/CDGuide.html Last revised October 30, 2012
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52
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53 \begin{tikzcd}
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54 ABC A \arrow[hook]{r}\arrow[two heads]{rd}
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55 &B \arrow[dotted]{d}\arrow[hookleftarrow]{r}
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56 &C \arrow[two heads]{ld}\\ D &D
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57 \end{tikzcd}
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58
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59
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60 \begin{tikzcd}
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61 A \arrow[hook]{r}{u}[swap]{b}
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62 Aub Bub C \arrow[two heads]{rd}{u}[swap]{b}
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63 &B \arrow[dotted]{d}{r}[swap]{l}
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64 \arrow[hookleftarrow]{r}{u}[swap]{b}
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65 D &C \arrow[two heads]{ld}{b}[swap]{u}\\ &D
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66 \end{tikzcd}
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67
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68 \begin{tikzcd}
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69 A\arrow{r}\arrow{d}
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70 &B\arrow{r}{\text{very long label}}\arrow{d}
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71 &C\arrow{d}\\
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72 DEF D\arrow{r}&E\arrow{r}&F
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73 \end{tikzcd}
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74
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75 % \begin{tikzcd}[column sep=large]
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76 % A\arrow{r}\arrow{d}
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77
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78
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79 \begin{tikzcd}
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80 A B A\arrow[bend left]{r}\arrow[bend right]{r}&B
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81 \end{tikzcd}
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82
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83 \begin{tikzcd}
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84 &A\arrow{ldd}[swap]{f}\arrow{rd}[description]{c}
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85 \arrow{rrd}[description]{d}
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86 \arrow{rrrd}[description]{e}\\
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87 &B\arrow{ld}\arrow{r}&C\arrow{r}&D\arrow{r}&E\\
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88 F
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89 \end{tikzcd}
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90
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91 \begin{tikzcd}
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92 T\arrow[bend left]{drr}{x}
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93 \arrow[bend right]{ddr}[swap]{y}
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94 \arrow[dotted]{dr}[description]{(x,y)} & & \\
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95 & X \times_Z Y \arrow{r}{p} \arrow{d}{q} & X \arrow{d}{f} \\
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96 & Y \arrow{r}{g} & Z
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97 \end{tikzcd}
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98
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99 \begin{tikzpicture}[>=angle 90]
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100 \matrix(a)[matrix of math nodes,
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101 row sep=3em, column sep=2.5em,
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102 text height=1.5ex, text depth=0.25ex]
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103 {A&B&C\\
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104 &D\\};
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105 \path[right hook->](a-1-1) edge (a-1-2);
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106 \path[->>](a-1-1) edge (a-2-2);
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107 \path[dotted,->](a-1-2) edge (a-2-2);
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108 \path[left hook->](a-1-3) edge (a-1-2);
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109 \path[->>](a-1-3) edge (a-2-2);
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110 \end{tikzpicture}
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111
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112
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113
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114 \begin{tikzpicture}
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115 \matrix(m)[matrix of math nodes,
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116 row sep=3em, column sep=2.8em,
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117 text height=1.5ex, text depth=0.25ex]
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118 {A&B\\};
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119 \path[->]
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120 (m-1-1) edge [bend left] (m-1-2)
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121 edge [bend left=40] (m-1-2)
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122 edge [bend left=60] (m-1-2)
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123 edge [bend left=80] (m-1-2)
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124 edge [bend right] (m-1-2);
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125 \end{tikzpicture}
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126
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127 \[
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128 \begin{tikzpicture}[descr/.style={fill=white}]
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129 \matrix(m)[matrix of math nodes, row sep=3em, column sep=2.8em, text height=1.5ex, text depth=0.25ex]
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130 {&A\\&B&C&D&E\\F\\};
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131 \path[->,font=\scriptsize]
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132 (m-1-2) edge node[above left] {$f$} (m-3-1)
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133 edge node[descr] {$c$} (m-2-3)
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134 edge node[descr] {$d$} (m-2-4)
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135 edge node[descr] {$e$} (m-2-5);
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136 \path[->]
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137 (m-2-2) edge (m-3-1)
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138 edge (m-2-3);
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139 \path[->]
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140 (m-2-3) edge (m-2-4);
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141 \path[->]
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142 (m-2-4) edge (m-2-5);
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143 \end{tikzpicture}
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144 \]
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145
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146 \[
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147 \begin{tikzpicture}[descr/.style={fill=white}]
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148 \matrix(m)[matrix of math nodes, row sep=3em, column sep=2.8em,
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149 text height=1.5ex, text depth=0.25ex]
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150 {T\\&X\times_Z Y&X\\&Y&Z\\};
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151 7
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152
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153 \path[->,font=\scriptsize]
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154 (m-1-1) edge [bend left=10] node[above] {$x$} (m-2-3)
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155 (m-1-1) edge [bend right=10] node[below] {$y$} (m-3-2);
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156 \path[->,dotted,font=\scriptsize]
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157 (m-1-1) edge node[descr] {$(x,y)$} (m-2-2);
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158 \path[->,font=\scriptsize]
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159 (m-2-2) edge node[below] {$p$} (m-2-3)
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160 (m-2-2) edge node[right] {$q$} (m-3-2);
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161 \path[->,font=\scriptsize]
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162 (m-2-3) edge node[right] {$f$} (m-3-3);
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163 \path[->,font=\scriptsize]
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164 (m-3-2) edge node[above] {$g$} (m-3-3);
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165 \end{tikzpicture}
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166 \]
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167
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168 \begin{tikzpicture}
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169 \node (A) at (-1,0) {$A$};
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170 \node (B) at (1,0) {$B$};
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171 \node at (0,0) {\rotatebox{270}{$\Rightarrow$}};
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172 \path[->,font=\scriptsize,>=angle 90]
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173 (A) edge [bend left] node[above] {$\alpha$} (B)
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174 edge [bend right] node[below] {$\beta$} (B);
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175 \end{tikzpicture}
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176
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177 \begin{tikzpicture}
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178 \node (P0) at (90:2.8cm) {$X\otimes (Y\otimes (Z\otimes T))$};
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179 \node (P1) at (90+72:2.5cm) {$X\otimes ((Y\otimes Z)\otimes T))$} ;
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180 \node (P2) at (90+2*72:2.5cm) {${(X\otimes (Y\otimes Z))}\otimes T$};
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181 \node (P3) at (90+3*72:2.5cm) {$((X\otimes Y){\otimes Z)\otimes T}$};
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182 \node (P4) at (90+4*72:2.5cm) {$(X\otimes Y)\otimes (Z\otimes T)$};
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183 \draw
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184 (P0) edge[->,>=angle 90] node[left] {$1\otimes\phi$} (P1)
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185 (P1) edge[->,>=angle 90] node[left] {$\phi$} (P2)
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186 (P2) edge[->,>=angle 90] node[above] {$\phi\otimes 1$} (P3)
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187 (P4) edge[->,>=angle 90] node[right] {$\phi$} (P3)
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188 (P0) edge[->,>=angle 90] node[right] {$\phi$} (P4);
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189 \end{tikzpicture}
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190
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191
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192 \begin{tikzpicture}
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193 \node (a) at (0,0) {$Y\times_X Y$};
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194 \node (b) at (2,0) {$Y$};
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195 \node (c) at (3.5,0) {$X$};
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196 \path[->,font=\scriptsize,>=angle 90]
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197 ([yshift= 2pt]a.east) edge node[above] {$p_1$} ([yshift= 2pt]b.west)
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198 ([yshift= -2pt]a.east) edge node[below] {$p_2$} ([yshift= -2pt]b.west)
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199 (b) edge (c);
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200 \end{tikzpicture}
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201
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202 \begin{tikzpicture}[descr/.style={fill=white},text height=1.5ex, text depth=0.25ex]
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203 \node (a) at (0,0) {$\mathsf{S}(Z)$};
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204 \node (b) at (2.5,0) {$\mathsf{S}(X)$};
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205 \node (c) at (5,0) {$\mathsf{S}(U).$};
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206 \path[->,font=\scriptsize,>=angle 90]
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207 ([yshift= 9pt]b.west) edge node[above] {$i^{\ast}$} ([yshift= 9pt]a.east)
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208 (a.east) edge node[descr] {$i_{\ast}$} (b.west)
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209 ([yshift= -9pt]b.west) edge node[below] {$i^!$} ([yshift= -9pt]a.east)
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210 ([yshift= 9pt]c.west) edge node[above] {$j_!$} ([yshift= 9pt]b.east)
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211 (b.east) edge node[descr] {$j^{\ast}$} (c.west)
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212 ([yshift= -9pt]c.west) edge node[below] {$j_*$} ([yshift= -9pt]b.east);
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213 \end{tikzpicture}
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214
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215
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216 \begin{tikzpicture}[>=angle 90,scale=2.2,text height=1.5ex, text depth=0.25ex]
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217 %%First place the nodes
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218 \node (k-1) at (0,3) {$0$};
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219 \node (k0) [right=of k-1] {$Ker f$};
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220 \node (k1) [right=of k0] {$Ker a$};
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221 \node (k2) [right=of k1] {$Ker b$};
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222 \node (k3) [right=of k2] {$Ker c$};
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223 \node (a1) [below=of k1] {$A$};
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224 \node (a2) [below=of k2] {$B$};
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225 \node (a3) [below=of k3] {$C$};
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226 \node (a4) [right=of a3] {$0$};
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227 \node (b1) [below=of a1] {$A’$};
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228 \node (b0) [left=of b1] {$0$};
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229 \node (b2) [below=of a2] {$B’$};
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230 \node (b3) [below=of a3] {$C’$};
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231 \node (c1) [below=of b1] {$Coker a$};
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232 \node (c2) [below=of b2] {$Coker b$};
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233 \node (c3) [below=of b3] {$Coker c$};
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234 \node (c4) [right=of c3] {$Coker g’$};
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235 \node (c5) [right=of c4] {$0$};
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236 %%Draw the red arrows
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237 \draw[->,red,font=\scriptsize]
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238 (k-1) edge (k0)
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239 (k0) edge (k1)
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240 (k1) edge (k2)
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241 (k2) edge (k3)
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242 (c1) edge (c2)
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243 (c2) edge (c3)
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244 (c3) edge (c4)
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245 (c4) edge (c5);
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246 %%Draw the curvy red arrow
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247 \draw[->,red]
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248 (k3) edge[out=0,in=180,red] node[pos=0.55,yshift=5pt] {$d$} (c1);
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249 %%Draw the black arrows
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250 \draw[->]
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251 (k1) edge (a1)
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252 (k2) edge (a2)
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253 (k3) edge (a3)
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254 (b1) edge (c1)
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255 (b2) edge (c2)
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256 (b3) edge (c3);
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257 %%Draw the thick blue arrows
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258 \draw[->,font=\scriptsize,blue,thick]
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259 (a1) edge node[auto] {$f$} (a2)
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260 (a2) edge node[auto] {$g$} (a3)
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261 (a3) edge (a4)
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262 (a1) edge node[auto] {$a$} (b1)
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263 (a2) edge node[auto] {$b$} (b2)
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264 (a3) edge node[auto] {$c$} (b3)
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265 (b0) edge (b1)
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266 (b1) edge node[below] {$f’$} (b2)
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267 (b2) edge node[below] {$g’$} (b3);
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268 \end{tikzpicture}
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269
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270
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271 \end{document}
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