From 8d2977cf52c3c4dadee4d3d5157f39ef102408af Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:08:15 +0200
Subject: [PATCH 01/37] Draw 3.1/sheets
---
src/content/3.1/its-all-about-morphisms.tex | 28 ++++++++++++++++++++-
1 file changed, 27 insertions(+), 1 deletion(-)
diff --git a/src/content/3.1/its-all-about-morphisms.tex b/src/content/3.1/its-all-about-morphisms.tex
index 53bdc047..a8a8c9a8 100644
--- a/src/content/3.1/its-all-about-morphisms.tex
+++ b/src/content/3.1/its-all-about-morphisms.tex
@@ -78,7 +78,33 @@ \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
From 229abbe2bb1f4db5557ae0f06b650c943b9cbb54 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:09:35 +0200
Subject: [PATCH 02/37] Draw 3.15/spanmul
---
.../3.15/monads-monoids-and-categories.tex | 22 ++++++++++++++++++-
1 file changed, 21 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index b87a16f1..4145e6b7 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -293,7 +293,27 @@ \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
From 969fc2bd132462df1df4d88854e3c74dba165325 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:12:24 +0200
Subject: [PATCH 03/37] Draw 3.6/assocmon
---
src/content/3.6/monads-categorically.tex | 6 +++++-
1 file changed, 5 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index 3012ca6e..a6bbcb44 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -276,7 +276,11 @@ \section{Monoidal Categories}
\begin{figure}[H]
\centering
-\includegraphics[width=0.5\textwidth]{images/assocmon.png}
+\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ (a\times a) \times a \arrow[rr, "\alpha"] & & a\times (a\times a) \\
+ a\times a \arrow[from=1-1, "\mu\times id"] & & a\times a \arrow[from=1-3, "id\times\mu"] \\
+ & a \arrow[from=2-1, "\mu"] \arrow[from=2-3, "\mu"'] & \\
+\end{tikzcd}
\end{figure}
\noindent
From 5022ee00250844150543493965587dbf2f0a75c7 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:13:15 +0200
Subject: [PATCH 04/37] Draw 3.6/horizcomp
---
src/content/3.6/monads-categorically.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index a6bbcb44..a2c64d25 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -400,7 +400,9 @@ \section{Monads as Monoids}
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/horizcomp.png}
+\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ C \arrow[r, bend left=50, "F"{name=U, above}] \arrow[r, bend right=50, "F'"{name=D, below}] & C \arrow[Rightarrow, from=U, to=D] \arrow[r, bend left=50, "G"{name=U, above}] \arrow[r, bend right=50, "G'"{name=D, below}] & C \arrow[Rightarrow, from=U, to=D]
+\end{tikzcd}
\end{figure}
\noindent
From 9efb3dcb54d7a2e368d08fd7ae553131d7e1dda3 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:13:39 +0200
Subject: [PATCH 05/37] Draw 3.6/unitlawcomp
---
src/content/3.6/monads-categorically.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index a2c64d25..66eb8a5f 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -429,7 +429,21 @@ \section{Monads as Monoids}
\begin{figure}[H]
\centering
-\includegraphics[width=0.5\textwidth]{images/unitlawcomp.png}
+\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ \def\colspace{1.5}
+ \def\rowspace{2}
+ \node (P0) at (0*\rowspace, 1*\colspace) {$T\circ I$};
+ \node (P1) at (1*\rowspace, 1*\colspace) {$T^2$};
+ \node (P2) at (2*\rowspace, 1*\colspace) {$I\circ T$};
+ \node (P3) at (1*\rowspace, 0*\colspace) {$T$};
+
+ \path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
+ (P0) edge node {$\eta\,\circ\, T$} (P1)
+ (P1) edge node {$T\,\circ\,\eta$} (P2)
+ (P0) edge node {} (P3)
+ (P1) edge node {$\eta$} (P3)
+ (P2) edge node {} (P3);
+\end{tikzpicture}
\end{figure}
\noindent
From 023ff19274ee8b7673d435cb02e5939ff55c53ce Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 18:13:51 +0200
Subject: [PATCH 06/37] Draw 3.6/unitlawcomp-1
---
src/content/3.6/monads-categorically.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index 66eb8a5f..445d247c 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -156,7 +156,21 @@
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/unitlawcomp-1.png}
+\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ \def\colspace{1.5}
+ \def\rowspace{2}
+ \node (P0) at (0*\rowspace, 1*\colspace) {$I\circ T$};
+ \node (P1) at (1*\rowspace, 1*\colspace) {$T^2$};
+ \node (P2) at (2*\rowspace, 1*\colspace) {$T\circ I$};
+ \node (P3) at (1*\rowspace, 0*\colspace) {$T$};
+
+ \path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
+ (P0) edge node {$\eta\,\circ\, T$} (P1)
+ (P1) edge node {$T\,\circ\,\eta$} (P2)
+ (P0) edge node {} (P3)
+ (P1) edge node {$\eta$} (P3)
+ (P2) edge node {} (P3);
+\end{tikzpicture}
\end{figure}
\noindent
From 0447a568d248009f8f488521daf1130f92978584 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:05:41 +0200
Subject: [PATCH 07/37] Draw 3.15/twocat
---
src/content/3.15/monads-monoids-and-categories.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 4145e6b7..4d56d98b 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -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}
From cfcc06faa937cd06093ea50f09c0ef51fb3f5644 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:06:00 +0200
Subject: [PATCH 08/37] Draw 3.15/span
---
src/content/3.15/monads-monoids-and-categories.tex | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 4d56d98b..a4ca6605 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -125,7 +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
From c9d0038903a5459e726048a2eeaa5aee4eabd3c2 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:06:13 +0200
Subject: [PATCH 09/37] Draw 3.15/compspan
---
.../3.15/monads-monoids-and-categories.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index a4ca6605..82780d21 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -150,7 +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
From d3f39febf6a131f70da772369eac1c7d21d4c525 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:06:27 +0200
Subject: [PATCH 10/37] Draw 3.15/pullspan
---
.../3.15/monads-monoids-and-categories.tex | 20 ++++++++++++++++++-
1 file changed, 19 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 82780d21..8db022a8 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -182,7 +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
From 19f6df51bab593b8440e040d395a8aec4f8d31a1 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:06:39 +0200
Subject: [PATCH 11/37] Draw 3.15/morphspan
---
.../3.15/monads-monoids-and-categories.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 8db022a8..92452015 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -214,7 +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}
From 9ac65b06c0809f3d9569c4897835b9346a64a20f Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:06:52 +0200
Subject: [PATCH 12/37] Draw 3.15/monad
---
src/content/3.15/monads-monoids-and-categories.tex | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 92452015..ab672832 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -265,7 +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
From 5e76102e59270ac8d2fd340c9d5a8ba85d53d5cf Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:07:05 +0200
Subject: [PATCH 13/37] Draw 3.15/bimonad
---
src/content/3.15/monads-monoids-and-categories.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index ab672832..823178f6 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -296,7 +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
From d48eae1d7ee8817aaff7fb93d60d730af5e4a82c Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:07:15 +0200
Subject: [PATCH 14/37] Draw 3.15/spanmonad
---
src/content/3.15/monads-monoids-and-categories.tex | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 823178f6..9be282f0 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -319,7 +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
From 02925f09880fb7dac2e9d4de248fc1254c5424f5 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:07:27 +0200
Subject: [PATCH 15/37] Draw 3.15/spanunit
---
.../3.15/monads-monoids-and-categories.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/3.15/monads-monoids-and-categories.tex b/src/content/3.15/monads-monoids-and-categories.tex
index 9be282f0..91dc02fd 100644
--- a/src/content/3.15/monads-monoids-and-categories.tex
+++ b/src/content/3.15/monads-monoids-and-categories.tex
@@ -352,7 +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
From cb86eda2d81a660648ab0a0e9d3fe5224c3d2407 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 19:26:00 +0200
Subject: [PATCH 16/37] Draw 2.1/productranking
---
src/content/2.1/declarative-programming.tex | 16 +++++++++++++++-
1 file changed, 15 insertions(+), 1 deletion(-)
diff --git a/src/content/2.1/declarative-programming.tex b/src/content/2.1/declarative-programming.tex
index 425fca13..b713880e 100644
--- a/src/content/2.1/declarative-programming.tex
+++ b/src/content/2.1/declarative-programming.tex
@@ -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
From 3913903afd2d17a3a8ad69fd9a1c42cf6670bf25 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Fri, 4 Oct 2019 20:37:26 +0200
Subject: [PATCH 17/37] Draw 3.1/3_naturality
---
src/content/3.1/its-all-about-morphisms.tex | 7 ++++++-
1 file changed, 6 insertions(+), 1 deletion(-)
diff --git a/src/content/3.1/its-all-about-morphisms.tex b/src/content/3.1/its-all-about-morphisms.tex
index a8a8c9a8..22869e07 100644
--- a/src/content/3.1/its-all-about-morphisms.tex
+++ b/src/content/3.1/its-all-about-morphisms.tex
@@ -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
From b821f1a890dfeea46009eac1f5fe4dc147ad43ef Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:48:26 +0200
Subject: [PATCH 18/37] Draw 1.10/3_naturality
---
src/content/1.10/natural-transformations.tex | 7 ++++++-
1 file changed, 6 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index 85f5b2d0..eb927c4d 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -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
From b8070d5bd62b100dbd5623801848c53034a21876 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:48:41 +0200
Subject: [PATCH 19/37] Draw 1.10/4_transport
---
src/content/1.10/natural-transformations.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index eb927c4d..c467fb65 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -100,7 +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
From 506d11439d7c1beff3559f116432cf2aeaa24b31 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:49:00 +0200
Subject: [PATCH 20/37] Draw 1.10/5_vertical
---
src/content/1.10/natural-transformations.tex | 6 +++++-
1 file changed, 5 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index c467fb65..2ed3ac76 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -414,7 +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
From 71a3461a9c8ccd39fd4fabfc7d91f7ac1eab8c9a Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:49:38 +0200
Subject: [PATCH 21/37] Draw 1.10/6_verticalnaturality
---
src/content/1.10/natural-transformations.tex | 8 +++++++-
1 file changed, 7 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index 2ed3ac76..3ef48df0 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -428,7 +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
From 0bfc3cfe6c8cecc0ac4a0a4e58ab8b6560dba505 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:49:51 +0200
Subject: [PATCH 22/37] Draw 1.10/6a_vertical
---
src/content/1.10/natural-transformations.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index 3ef48df0..cd4cd531 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -457,7 +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
From d6f098d36742b7eb8b6fd5fdc893953f61236884 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:50:14 +0200
Subject: [PATCH 23/37] Draw 1.10/10_horizontal
---
src/content/1.10/natural-transformations.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/1.10/natural-transformations.tex b/src/content/1.10/natural-transformations.tex
index cd4cd531..f535dd04 100644
--- a/src/content/1.10/natural-transformations.tex
+++ b/src/content/1.10/natural-transformations.tex
@@ -568,7 +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
From f29c860e383fc029e6ffdb39b128eba4aa3d5ddb Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:50:38 +0200
Subject: [PATCH 24/37] Draw 3.8/alg
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index 7effb5ee..25d6c36c 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -209,7 +209,10 @@ \section{Category of F-Algebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/alg.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F a \arrow[r, "F m"] \arrow[d, "f"] & F b \arrow[d, "g"] \\
+ a \arrow[r, "m"] & b \\
+\end{tikzcd}
\end{figure}
\noindent
From afca8329f1f265158e5a2536b9b758eb4e20e49e Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:09 +0200
Subject: [PATCH 25/37] Draw 3.8/alg2
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index 25d6c36c..44adc215 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -231,7 +231,10 @@ \section{Category of F-Algebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/alg2.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F i \arrow[r, "F m"] \arrow[d, "j"] & Fa \arrow[d, "f"] \\
+ i \arrow[r, "m"] & a \\
+\end{tikzcd}
\end{figure}
\noindent
From 35d18826b2d722b8ffc366306a2aca2d4cde0567 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:16 +0200
Subject: [PATCH 26/37] Draw 3.8/alg3a
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index 44adc215..98b81fe1 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -249,7 +249,10 @@ \section{Category of F-Algebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/alg3a.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F i \arrow[r, "F m"] \arrow[d, "j"] & F(F i) \arrow[d, "F j"] \\
+ i \arrow[r, "m"] & Fi \\
+\end{tikzcd}
\end{figure}
\noindent
From 42d2631efbbcd4ce21bf991c211fca5044135c73 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:23 +0200
Subject: [PATCH 27/37] Draw 3.8/alg3
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index 98b81fe1..f1c0d1b6 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -261,7 +261,10 @@ \section{Category of F-Algebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/alg3.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F(F i) \arrow[r, "F j"] \arrow[d, "F j"] & F i \arrow[d, "j"] \\
+ F i \arrow[r, "j"] & i \\
+\end{tikzcd}
\end{figure}
\noindent
From efc48a9ed25eaf551a8442789b09647aea7158ee Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:28 +0200
Subject: [PATCH 28/37] Draw 3.8/alg4
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index f1c0d1b6..01fc8db6 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -274,7 +274,10 @@ \section{Category of F-Algebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.6\textwidth]{images/alg4.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F i \arrow[r, "F m"] \arrow[d, "j"] & F(F i) \arrow[d, "F j"] \arrow[r, "F j"] & F i \arrow[d, "j"] \\
+ i \arrow[r, "m"] & F i \arrow[r, "j"] & i\\
+\end{tikzcd}
\end{figure}
\noindent
From bdf2df9305dd7fc25ea740d08fc922d10a5a2c7e Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:40 +0200
Subject: [PATCH 29/37] Draw 3.8/alg5
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index 01fc8db6..e560c000 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -334,7 +334,10 @@ \section{Catamorphisms}
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/alg5.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ f(Fix\,f) \arrow[r, "f\,map\,m"] \arrow[d, "Fix"] & fa \arrow[d, "alg"] \\
+ Fix\,f \arrow[r, "m"] & a
+\end{tikzcd}
\end{figure}
\noindent
From c760e9add873d7e2c5ec95243bb3b45a65bf85da Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:46 +0200
Subject: [PATCH 30/37] Draw 3.8/alg6
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index e560c000..d8bddad9 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -351,7 +351,10 @@ \section{Catamorphisms}
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/alg6.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ f(Fix\,f) \arrow[r, "f\,map\,m"] \arrow[from=d, "unFix"] & fa \arrow[d, "alg"] \\
+ Fix\,f \arrow[r, "m"] & a
+\end{tikzcd}
\end{figure}
\noindent
From 51f7201fbe28ab6131de798d5dba40d5677b6c96 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 09:51:56 +0200
Subject: [PATCH 31/37] Draw 3.8/alg7
---
src/content/3.8/f-algebras.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.8/f-algebras.tex b/src/content/3.8/f-algebras.tex
index d8bddad9..8f356a80 100644
--- a/src/content/3.8/f-algebras.tex
+++ b/src/content/3.8/f-algebras.tex
@@ -453,7 +453,10 @@ \section{Coalgebras}
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/alg7.png}
+\begin{tikzcd}[column sep=large,row sep=large,cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ F t & F a \arrow[l, "F m"{above}] \\
+ t \arrow[u, "u"{right}] & a \arrow[u, "f"{right}] \arrow[l, "m"{above}]
+\end{tikzcd}
\end{figure}
\noindent
From 3b477ab8dc9aa14cef5de5b0bb14fda2355f2eda Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:29:31 +0200
Subject: [PATCH 32/37] Draw 3.6/assoc1
---
src/content/3.6/monads-categorically.tex | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index 445d247c..a6799e72 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -115,7 +115,9 @@
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/assoc1.png}
+\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ C \arrow[r, bend left=50, "T^2"{name=U, above}] \arrow[r, bend right=50, "T"{name=D, below}] & C \arrow[Rightarrow, from=U, to=D, "\mu"] \arrow[r, bend left=50, "T"{name=U, above}] \arrow[r, bend right=50, "T"{name=D, below}] & C \arrow[Rightarrow, from=U, to=D, "I_T"]
+\end{tikzcd}
\end{figure}
\noindent
From 8fd22e27faa161555d22067608d70f3cc3db6200 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:29:38 +0200
Subject: [PATCH 33/37] Draw 3.6/assoc2
---
src/content/3.6/monads-categorically.tex | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index a6799e72..b81bec42 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -134,7 +134,17 @@
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/assoc2.png}
+\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ \def\colspace{1.8}
+ \def\rowspace{2}
+ \node (P0) at (0*\rowspace, 1*\colspace) {$T^3$};
+ \node (P1) at (1*\rowspace, 0*\colspace) {$T$};
+ \node (P2) at (0*\rowspace, 0*\colspace) {$T^2$};
+
+ \path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
+ (P0) edge node {$T\circ\mu$} (P2)
+ (P2) edge node {$\mu$} (P1);
+\end{tikzpicture}
\end{figure}
\noindent
From 479211cceb7312e14c66ade8f257b5a8a2e0bf67 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:29:44 +0200
Subject: [PATCH 34/37] Draw 3.6/assoc
---
src/content/3.6/monads-categorically.tex | 15 ++++++++++++++-
1 file changed, 14 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index b81bec42..a3d123bd 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -155,7 +155,20 @@
\begin{figure}[H]
\centering
-\includegraphics[width=0.3\textwidth]{images/assoc.png}
+\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ \def\colspace{1.8}
+ \def\rowspace{2}
+ \node (P0) at (0*\rowspace, 1*\colspace) {$T^3$};
+ \node (P1) at (1*\rowspace, 0*\colspace) {$T$};
+ \node (P2) at (0*\rowspace, 0*\colspace) {$T^2$};
+ \node (P4) at (1*\rowspace, 1*\colspace) {$T^2$};
+
+ \path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
+ (P0) edge node {$T\circ\mu$} (P2)
+ (P2) edge node {$\mu$} (P1)
+ (P0) edge node {$T\circ\mu$} (P4)
+ (P4) edge node {$\mu$} (P1);
+\end{tikzpicture}
\end{figure}
\noindent
From 7f2333217fbf91f6246fae7fc889834f6986667f Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:30:28 +0200
Subject: [PATCH 35/37] Draw 3.6/assoctensor
---
src/content/3.6/monads-categorically.tex | 6 +++++-
1 file changed, 5 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index a3d123bd..62857867 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -394,7 +394,11 @@ \section{Monoid in a Monoidal Category}
\begin{figure}[H]
\centering
-\includegraphics[width=0.5\textwidth]{images/assoctensor.jpg}
+\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ (m\otimes m) \otimes m \arrow[rr, "\alpha"] & & m\otimes (m\otimes m) \\
+ m\otimes m \arrow[from=1-1, "\mu\otimes id"] & & m\otimes m \arrow[from=1-3, "id\otimes\mu"] \\
+ & m \arrow[from=2-1, "\mu"] \arrow[from=2-3, "\mu"'] & \\
+\end{tikzcd}
\end{figure}
\begin{figure}[H]
From 523b5e20324817b94d764dacdd48ebe4cd3b68cd Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:30:52 +0200
Subject: [PATCH 36/37] Draw 3.6/unitmon
---
src/content/3.6/monads-categorically.tex | 5 ++++-
1 file changed, 4 insertions(+), 1 deletion(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index 62857867..8ad6bfc5 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -403,7 +403,10 @@ \section{Monoid in a Monoidal Category}
\begin{figure}[H]
\centering
-\includegraphics[width=0.5\textwidth]{images/unitmon.jpg}
+\begin{tikzcd}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ i\otimes m \arrow[r, "\eta\otimes id"] \arrow[dr, "\lambda"] & m\otimes m \arrow[d, "\mu"] & m\otimes i \arrow[l, "id\otimes\eta"] \arrow[dl, "\rho"] \\
+ & m & \\
+\end{tikzcd}
\end{figure}
\noindent
From 497eda42b17e1df1217d3cc56c38460ebaabad29 Mon Sep 17 00:00:00 2001
From: Enrico Paganin <enrico.paganin@mail.com>
Date: Mon, 7 Oct 2019 10:31:08 +0200
Subject: [PATCH 37/37] Draw 3.6/assoc
---
src/content/3.6/monads-categorically.tex | 20 ++++++++++++++++++--
1 file changed, 18 insertions(+), 2 deletions(-)
diff --git a/src/content/3.6/monads-categorically.tex b/src/content/3.6/monads-categorically.tex
index 8ad6bfc5..b3ce0d4a 100644
--- a/src/content/3.6/monads-categorically.tex
+++ b/src/content/3.6/monads-categorically.tex
@@ -470,13 +470,29 @@ \section{Monads as Monoids}
\begin{figure}[H]
\centering
-\includegraphics[width=0.4\textwidth]{images/assoc.png}
+\begin{figure}[H]
+\centering
+\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
+ \def\colspace{1.8}
+ \def\rowspace{2}
+ \node (P0) at (0*\rowspace, 1*\colspace) {$T^3$};
+ \node (P1) at (1*\rowspace, 0*\colspace) {$T$};
+ \node (P2) at (0*\rowspace, 0*\colspace) {$T^2$};
+ \node (P4) at (1*\rowspace, 1*\colspace) {$T^2$};
+
+ \path[commutative diagrams/.cd,every arrow, every label,line width=0.2mm]
+ (P0) edge node {$T\circ\mu$} (P2)
+ (P2) edge node {$\mu$} (P1)
+ (P0) edge node {$T\circ\mu$} (P4)
+ (P4) edge node {$\mu$} (P1);
+\end{tikzpicture}
+\end{figure}
\end{figure}
\begin{figure}[H]
\centering
\begin{tikzpicture}[cells={nodes={font=\fontsize{10}{6}\selectfont}}]
- \def\colspace{1.5}
+ \def\colspace{1.8}
\def\rowspace{2}
\node (P0) at (0*\rowspace, 1*\colspace) {$T\circ I$};
\node (P1) at (1*\rowspace, 1*\colspace) {$T^2$};