NUCT0005.tex
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\begin{document}
\centering
\begin{figure}
\centering
\includegraphics[width=10cm, height=2cm]{fracture.png}
\end{figure}
Figure: The formation of many. Previously less understood.
%Unrelated to the quote.
\raggedright
\begin{wrapfigure}{l}{0.5\textwidth}
\section*{Preface}
This book is meant to be an introduction to the topics needed for \textit{Category Theory in Context}, I think. It is meant to cover all the topics leading up to caregory theory, including topics in naive set theory, algebra, topology, algebraic topology, and "differential and algebraic geometry". Hey maybe I'm not supposed to know this. The first strip wasn't meant to be a book cover, then subsequent strips just happened to follow book contents order. Hey maybe I'm not supposed to know this. Actually, who am I? Let's leave that as an exercise. Text text text text text text text text text text text text text text text text text text text \TeX t text text text
% not like Hyperego...
\subsection*{How to read this book:}
\begin{tikzpicture}
\draw[thick, ->] (6.7, 9.4) -- (6.2, 6.0);
\draw[thick, ->] (6.5, 9.7) -- (4.3, 2.2);
\draw[thick, ->] (9.5, 8.2) -- (6.7, 7.5);
\draw[thick, ->] (3.8, 8.3) -- (7.3, 5.0);
\draw[thick, ->] (7.4, 7.1) -- (4.5, 2.7);
\draw[thick, ->] (9.7, 4.9) -- (2.3, 7.4);
\draw[thick, ->] (6.9, 3.7) -- (6.7, 2.6);
\draw[thick, ->] (4.6, 5.1) -- (2.7, 9.8);
\draw[thick, ->] (6.6, 8.0) -- (8.8, 7.6);
\draw[thick, ->] (4.5, 2.2) -- (7.4, 9.5);
\draw[thick, ->] (8.8, 8.3) -- (6.0, 7.1);
\draw[thick, ->] (4.9, 3.8) -- (4.8, 6.5);
\draw[thick, ->] (4.4, 5.4) -- (2.9, 5.1);
\draw[thick, ->] (3.5, 7.7) -- (9.7, 5.1);
\draw[thick, ->] (3.8, 8.8) -- (8.4, 8.7);
\draw[thick, ->] (5.5, 4.7) -- (6.4, 9.3);
\draw[thick, ->] (6.1, 5.9) -- (3.8, 2.1);
\end{tikzpicture}
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\epigraph{When Eilenberg and Mac Lane created category theory, Steenrod saw he could use their way of emphasizing morphisms at least as much as objects. He happily said this “abstract nonsense” was the key to solving his problem.}{Colin McLarty}
\raggedright
\textit{Hyperego:} Wow...
\vspace{1em}
I think I know enough \LaTeX\ to continue.
\vspace{0.5em}
Looks like we're in a category theory book. This comic isn't supposed to be about that despite its name \ldots
\vspace{0.5em}
So, how do I fix this?
\textit{Adjudicator:} The comic \\
\textit{Hyperego:} Ahhh!!!
\vspace{5pt}
\textit{Adjudicator:} currently lies in the image of CTCreation, which is a mapping from \textbf{Known CT} to \textbf{Written CT}. It's defined by
\begin{gather*}
\text{CTCreation : } \textbf{Known CT} \times \textbf{Random}_{low} \rightarrow \textbf{Written CT} \\
\text{and} \\
\textbf{CTCreation} = \textbf{Creativity}^{dual}
\end{gather*}
%This is clearly not 4o-mini. ALS
o, %the author doesn't know CT nor is this a research paper lol
\textit{Hyperego:} I didn't think you listened to me. Or still existed. Ok here we go:
\vspace{0.5em}
The comic --
\vspace{0.5em}
Hmmm \ldots
\vspace{0.5em}
\st{Adjuncticating it, I'm.},
You didn't answer me, how do I fix this?
\vspace{0.5em}
\textit{Adjudicator:}
\vspace{0.5em}
**1. Break the functor itself:**
Make CTCreation undefined or inconsistent. Introduce elements that can't be processed by it at all — things that aren't in Known CT × Random\_{low}, or things that break the mapping rules. Create a "type error" in the construction.
\begin{tikzpicture}
\draw[thick, ->] (2.9, 13.7) -- (0.2, 4.0);
\draw[thick, ->] (19.6, 8.0) -- (7.0, 17.3);
\draw[thick, ->] (12.2, 2.7) -- (20, 4.7);
\draw[thick, ->] (2.8, 7.0) -- (7.2, 10.4);
\draw[thick, ->] (7.4, 11.7) -- (17.2, 12.9);
\draw[thick, ->] (13.7, 12.8) -- (2.8, 15.6);
\draw[thick, ->] (16.3, 19.7) -- (11.7, 11.9);
\node[rotate=-307] at (11.9,17.4) {$\mathcal{T}$};
\end{tikzpicture}
**2. Change what category the comic lives in:**
Maybe the comic isn't actually an object in Written CT at all. Redefine its categorical home. It could turn out the whole analysis was wrong — the comic is actually in Webcomics or Stories or something, and CTCreation was never the right lens.
% "Maybe" saves this comic.
\vspace{0.5em}
[...]
\vspace{0.5em}
\textit{Hyperego:} Neat. How do I do these without breaking more things? \st{Immutability is looking nice right now}
\vspace{0.5em}
\textit{Adjudicator:}
\vspace{0.5em}
[...]
\vspace{0.5em}
**Use a "realization" or "discovery" rather than a retcon:**
\vspace{0.5em}
"I thought we were in Written CT, but look — [observe some property]"
\vspace{0.5em}
"Written CT objects can't have [this property], so we must actually be in [different category] ................................".......................................................
\vfill
$\fcolorbox{black}{white}{\textcolor{black}{Next Up: Category Theory}}$ $\in$ ob(\textbf{[different category]}). \\
Next Up: Category Theory is in \textbf{[different category]}.
\vspace{1em}
\centering
\begin{figure}[h]
\centering
\includegraphics[width=9cm]{plot.png}
\end{figure}
Figure: The plot of many as of 12 July, 2025. Long outdated.
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