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Redraw commutative diagrams with Tikz #219

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8d2977c
Draw 3.1/sheets
platipo Oct 4, 2019
229abbe
Draw 3.15/spanmul
platipo Oct 4, 2019
969fc2b
Draw 3.6/assocmon
platipo Oct 4, 2019
5022ee0
Draw 3.6/horizcomp
platipo Oct 4, 2019
9efb3dc
Draw 3.6/unitlawcomp
platipo Oct 4, 2019
023ff19
Draw 3.6/unitlawcomp-1
platipo Oct 4, 2019
0447a56
Draw 3.15/twocat
platipo Oct 4, 2019
cfcc06f
Draw 3.15/span
platipo Oct 4, 2019
c9d0038
Draw 3.15/compspan
platipo Oct 4, 2019
d3f39fe
Draw 3.15/pullspan
platipo Oct 4, 2019
19f6df5
Draw 3.15/morphspan
platipo Oct 4, 2019
9ac65b0
Draw 3.15/monad
platipo Oct 4, 2019
5e76102
Draw 3.15/bimonad
platipo Oct 4, 2019
d48eae1
Draw 3.15/spanmonad
platipo Oct 4, 2019
02925f0
Draw 3.15/spanunit
platipo Oct 4, 2019
cb86eda
Draw 2.1/productranking
platipo Oct 4, 2019
3913903
Draw 3.1/3_naturality
platipo Oct 4, 2019
b821f1a
Draw 1.10/3_naturality
platipo Oct 7, 2019
b8070d5
Draw 1.10/4_transport
platipo Oct 7, 2019
506d114
Draw 1.10/5_vertical
platipo Oct 7, 2019
71a3461
Draw 1.10/6_verticalnaturality
platipo Oct 7, 2019
0bfc3cf
Draw 1.10/6a_vertical
platipo Oct 7, 2019
d6f098d
Draw 1.10/10_horizontal
platipo Oct 7, 2019
f29c860
Draw 3.8/alg
platipo Oct 7, 2019
afca832
Draw 3.8/alg2
platipo Oct 7, 2019
35d1882
Draw 3.8/alg3a
platipo Oct 7, 2019
42d2631
Draw 3.8/alg3
platipo Oct 7, 2019
efc48a9
Draw 3.8/alg4
platipo Oct 7, 2019
bdf2df9
Draw 3.8/alg5
platipo Oct 7, 2019
c760e9a
Draw 3.8/alg6
platipo Oct 7, 2019
51f7201
Draw 3.8/alg7
platipo Oct 7, 2019
3b477ab
Draw 3.6/assoc1
platipo Oct 7, 2019
8fd22e2
Draw 3.6/assoc2
platipo Oct 7, 2019
479211c
Draw 3.6/assoc
platipo Oct 7, 2019
7f23332
Draw 3.6/assoctensor
platipo Oct 7, 2019
523b5e2
Draw 3.6/unitmon
platipo Oct 7, 2019
497eda4
Draw 3.6/assoc
platipo Oct 7, 2019
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34 changes: 28 additions & 6 deletions src/content/1.10/natural-transformations.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -77,7 +77,12 @@

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/3_naturality.jpg}
\begin{tikzcd}[row sep=large,column sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
& F a \arrow[dd, dashed, pos=0.7, "F f"] \arrow[dr, "\alpha_a"] & \\
a \arrow[rr, crossing over] \arrow[ur] \arrow[dd, "f"] & & G a \arrow[dd, "G_f"] \\
& F b \arrow[dr, "\alpha_b"] & \\
b \arrow[rr] \arrow[ur] & & G b \\
\end{tikzcd}
\end{figure}

\noindent
Expand All @@ -95,7 +100,10 @@

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/4_transport.jpg}
\begin{tikzcd}[row sep=huge,column sep=huge,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
F a \arrow[r, "\alpha_a"] \arrow[d, swap, bend right=30, "F f"] & G a \arrow[d, "G f"]\\
F b \arrow[r, dashed, "\alpha_b"] \arrow[u, swap, dashed, bend right=30, "(F f)^{-1}"] & G b
\end{tikzcd}
\end{figure}

\noindent
Expand Down Expand Up @@ -406,7 +414,11 @@ \section{Functor Category}

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/5_vertical.jpg}
\begin{tikzcd}[row sep=large,column sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
& & F a \arrow[dr, "\alpha a"] \arrow[dd, dashed, out=0, in=0, looseness=2.5, "(\beta\cdot\alpha) a"] & \\
a \arrow[urr, "F"] \arrow[rrr, "G"] \arrow[drr, "H"] & & & G a \arrow[dl, "\beta a"] \\
& & H a & \\
\end{tikzcd}
\end{figure}

\noindent
Expand All @@ -416,7 +428,13 @@ \section{Functor Category}

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/6_verticalnaturality.jpg}
\begin{tikzcd}[row sep=large,column sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
& & & F a \arrow[dl, "\alpha_a"] \arrow[dd, "F f"] \\
a \arrow[urrr, "F"] \arrow[rr, "G"] \arrow[dr, "H"] \arrow[dd, "f"] & & G a \arrow[dl, "\beta_a"] & \\
& H a & & F b \arrow[dl, "\alpha_b"] \\
b \arrow[urrr, dashed] \arrow[rr, dashed] \arrow[dr] & & G b \arrow[dl, "\beta_b"] \arrow[from=uu, crossing over, "G f"] & \\
& H b \arrow[from=uu, crossing over, pos=0.41, "H f"] & & \\
\end{tikzcd}
\end{figure}

\noindent
Expand All @@ -439,7 +457,9 @@ \section{Functor Category}

\begin{figure}[H]
\centering
\includegraphics[width=0.3\textwidth]{images/6a_vertical.jpg}
\begin{tikzcd}[column sep=huge,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\mathcal{C} \arrow[r, bend left=65, pos=.37, "F"] \arrow[r, pos=.2, "G"] \arrow[r, bend right=65, pos=.2, "H"] \arrow[r, bend left=65, ""{name=U, below}] \arrow[r, ""{name=M, below}] \arrow[r, bend right=65, ""{name=D, below}] & \mathcal{D} \arrow[Rightarrow, from=U, to=M, "\alpha"] \arrow[Rightarrow, from=M, to=D, "\beta"]
\end{tikzcd}
\end{figure}

\noindent
Expand Down Expand Up @@ -548,7 +568,9 @@ \section{2-Categories}

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/10_horizontal.jpg}
\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\mathcal{C} \arrow[r, bend left=50, "F"{name=U, above}] \arrow[r, bend right=50, "F'"{name=D, below}] & \mathcal{D} \arrow[Rightarrow, from=U, to=D, "\alpha"] \arrow[r, bend left=50, "G"{name=U, above}] \arrow[r, bend right=50, "G'"{name=D, below}] & \mathcal{E} \arrow[Rightarrow, from=U, to=D, "\beta"]
\end{tikzcd}
\end{figure}

\noindent
Expand Down
16 changes: 15 additions & 1 deletion src/content/2.1/declarative-programming.tex
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -181,7 +181,21 @@

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/productranking.jpg}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1}
\def\rowspace{1}
\node (P0) at (2*\rowspace, 2*\colspace) {$c'$};
\node (P12) at (2*\rowspace, 0.8*\colspace) {$c$};
\node (P3) at (0*\rowspace, 0*\colspace) {$a$};
\node (P5) at (4*\rowspace, 0*\colspace) {$b$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node["$p'$", above] {} (P3)
(P0) edge node["$q'$"] {} (P5)
(P12) edge node[below, "$p$"] {} (P3)
(P12) edge node[below, "$q$"] {} (P5)
(P0) edge[commutative diagrams/dashrightarrow, "$m$", swap] (P12);
\end{tikzpicture}
\end{figure}

\noindent
Expand Down
35 changes: 33 additions & 2 deletions src/content/3.1/its-all-about-morphisms.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -60,7 +60,12 @@ \section{Natural Transformations}

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/3_naturality.jpg}
\begin{tikzcd}[row sep=large,column sep=large]
& F_a \arrow[dd, dashed, pos=0.7, "F_f"] \arrow[dr, "\alpha_a"] & \\
a \arrow[rr, crossing over] \arrow[ur] \arrow[dd, "f"] & & G_a \arrow[dd, "G_f"] \\
& F_b \arrow[dr, "\alpha_b"] & \\
b \arrow[rr] \arrow[ur] & & G_b \\
\end{tikzcd}
\end{figure}

\noindent
Expand All @@ -78,7 +83,33 @@ \section{Natural Transformations}

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/sheets.png}
\begin{tikzpicture}[scale=1.15]
\def\between{0.85}
\def\length{1.7}
\def\arclen{1.3}
\draw (-\between/2,0) arc (0:-90:1) -- (-1-\between/2,\length)
arc (-90:0:1) -- cycle;
\draw (\between/2,0) arc (-180:-90:1) -- (1+\between/2,\length)
arc (-90:-180:1) -- cycle;

\def\nodecoordright{\between/2+0.5}
\def\nodecoordleft{-\between/2-0.5}
\def\nodecoordhigh{\length*0.85}
\def\nodecoordlow{\length*0}
\node (Ga) at (\nodecoordright, \nodecoordhigh) {$Ga$};
\node (Fa) at (\nodecoordleft, \nodecoordhigh) {$Fa$};
\node (Gb) at (\nodecoordright, \nodecoordlow) {$Gb$};
\node (Fb) at (\nodecoordleft, \nodecoordlow) {$Fb$};
\node (a) at (4*\nodecoordleft, \nodecoordhigh) {$a$};
\node (b) at (4*\nodecoordleft, \nodecoordlow) {$b$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(Fa) edge node {$\alpha_a$} (Ga)
(Fa) edge node[swap] {$Ff$} (Fb)
(Ga) edge node {$Gf$} (Gb)
(Fb) edge node {$\alpha_b$} (Gb)
(a) edge node[swap] {$f$} (b);
\end{tikzpicture}
\end{figure}

\noindent
Expand Down
134 changes: 124 additions & 10 deletions src/content/3.15/monads-monoids-and-categories.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -48,7 +48,9 @@ \section{Bicategories}

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/twocat.png}
\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
a \arrow[r, bend left=50, "f"{name=U, above}] & b \arrow[l, bend left=50, "g"{name=D}] \arrow[Rightarrow, from=U, to=D, "\alpha"]
\end{tikzcd}
\caption{$0$-cells $a, b$; $1$-cells $f, g$; and a $2$-cell $\alpha$.}
\end{figure}

Expand Down Expand Up @@ -123,7 +125,17 @@ \section{Bicategories}

\begin{figure}[H]
\centering
\includegraphics[width=0.35\textwidth]{images/span.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.5}
\node (x) at (2*\rowspace, 2*\colspace) {$x$};
\node (a) at (1*\rowspace, 1*\colspace) {$a$};
\node (b) at (3*\rowspace, 1*\colspace) {$b$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(x) edge node[swap] {$f$} (a)
(x) edge node {$g$} (b);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -138,7 +150,21 @@ \section{Bicategories}

\begin{figure}[H]
\centering
\includegraphics[width=0.5\textwidth]{images/compspan.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.5}
\node (P1) at (1*\rowspace, 1*\colspace) {$x$};
\node (P2) at (3*\rowspace, 1*\colspace) {$y$};
\node (P3) at (0*\rowspace, 0*\colspace) {$a$};
\node (P4) at (2*\rowspace, 0*\colspace) {$b$};
\node (P5) at (4*\rowspace, 0*\colspace) {$c$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P1) edge node[swap] {$f$} (P3)
(P1) edge node {$g$} (P4)
(P2) edge node[swap] {$f'$} (P4)
(P2) edge node {$g'$} (P5);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -156,7 +182,25 @@ \section{Bicategories}

\begin{figure}[H]
\centering
\includegraphics[width=0.5\textwidth]{images/pullspan.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.5}
\node (z) at (2*\rowspace, 2*\colspace) {$z$};
\node (x) at (1*\rowspace, 1*\colspace) {$x$};
\node (y) at (3*\rowspace, 1*\colspace) {$y$};
\node (a) at (0*\rowspace, 0*\colspace) {$a$};
\node (b) at (2*\rowspace, 0*\colspace) {$b$};
\node (c) at (4*\rowspace, 0*\colspace) {$c$};
\node (P0b) at (2*\rowspace, 1.7*\colspace) {\rotatebox[origin=c]{-45}{\Large$\lrcorner$}};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(z) edge node[swap] {$h$} (x)
(z) edge node {$h'$} (y)
(x) edge node[swap] {$f$} (a)
(x) edge node[swap] {$g$} (b)
(y) edge node {$f'$} (b)
(y) edge node {$g'$} (c);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -170,7 +214,21 @@ \section{Bicategories}

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/morphspan.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.2}
\node (P0) at (2*\rowspace, 2*\colspace) {$x$};
\node (P12) at (2*\rowspace, 0.8*\colspace) {$y$};
\node (P3) at (0*\rowspace, 0*\colspace) {$a$};
\node (P5) at (4*\rowspace, 0*\colspace) {$b$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node {} (P3)
(P0) edge node {} (P5)
(P12) edge node {} (P3)
(P12) edge node[swap] {} (P5)
(P0) edge[commutative diagrams/Rightarrow, "$h$"] (P12);
\end{tikzpicture}
\caption{A $2$-cell in $\cat{Span}$.}
\end{figure}

Expand Down Expand Up @@ -207,7 +265,17 @@ \section{Monads}

\begin{figure}[H]
\centering
\includegraphics[width=0.3\textwidth]{images/monad.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.8}
\def\rowspace{1.8}
\node (P0) at (1*\rowspace, 1*\colspace) {$T\circ T$};
\node (P1) at (1*\rowspace, 0*\colspace) {$T$};
\node (P2) at (0*\rowspace, 0*\colspace) {$I$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node {$\mu$} (P1)
(P2) edge node {$\eta$} (P1);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -228,7 +296,9 @@ \section{Monads}

\begin{figure}[H]
\centering
\includegraphics[width=0.3\textwidth]{images/bimonad.png}
\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
a \arrow[loop above, "id"{name=id}] \arrow[loop, "T"{name=T}, looseness=18, out=130,in=50] \arrow[loop, "T\circ T"{name=T2}, looseness=25, out=140,in=40] \arrow[Rightarrow, from=id, to=T, "\eta"] \arrow[Rightarrow, from=T2, to=T, "\mu"']
\end{tikzcd}
\end{figure}

\noindent
Expand All @@ -249,7 +319,17 @@ \section{Monads}

\begin{figure}[H]
\centering
\includegraphics[width=0.3\textwidth]{images/spanmonad.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.5}
\node (P0) at (2*\rowspace, 2*\colspace) {$Arr$};
\node (P1) at (1*\rowspace, 1*\colspace) {$Ob$};
\node (P2) at (3*\rowspace, 1*\colspace) {$Ob$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node[swap] {$dom$} (P1)
(P0) edge node {$cod$} (P2);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -272,7 +352,21 @@ \section{Monads}

\begin{figure}[H]
\centering
\includegraphics[width=0.4\textwidth]{images/spanunit.png}
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
\def\colspace{1.2}
\def\rowspace{1.2}
\node (P0) at (2*\rowspace, 2*\colspace) {$Ob$};
\node (P12) at (2*\rowspace, 0.8*\colspace) {$Arr$};
\node (P3) at (0*\rowspace, 0*\colspace) {$Ob$};
\node (P5) at (4*\rowspace, 0*\colspace) {$Ob$};

\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node[swap] {$id$} (P3)
(P0) edge node {$id$} (P5)
(P12) edge node {$dom$} (P3)
(P12) edge node[swap] {$cod$} (P5)
(P0) edge[commutative diagrams/Rightarrow, "$\eta$"] (P12);
\end{tikzpicture}
\end{figure}

\noindent
Expand All @@ -293,7 +387,27 @@ \section{Monads}

\begin{figure}[H]
\centering
\includegraphics[width=0.5\textwidth]{images/spanmul.png}
\begin{tikzpicture}[cells={nodes={font=\bfseries}}]
\def\colspace{1.2}
\def\rowspace{1.5}
\node (P0) at (2*\rowspace, 2*\colspace) {$Arr\otimes Arr$};
\node (P1) at (1*\rowspace, 1*\colspace) {$Arr$};
\node (P2) at (3*\rowspace, 1*\colspace) {$Arr$};
\node (P3) at (0*\rowspace, 0*\colspace) {$Ob$};
\node (P4) at (2*\rowspace, 0*\colspace) {$Ob$};
\node (P5) at (4*\rowspace, 0*\colspace) {$Ob$};
\node (P0b) at (2*\rowspace, 1.7*\colspace) {\rotatebox[origin=c]{-45}{$\lrcorner$}};


\path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
(P0) edge node {} (P1)
(P0) edge node {} (P2)
(P1) edge node[swap] {$dom$} (P3)
(P1) edge node[swap] {$cod$} (P4)
(P2) edge node[swap] {$dom$} (P4)
(P2) edge node[swap] {$cod$} (P5);
\end{tikzpicture}

\end{figure}

\noindent
Expand Down
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