Added notation pages for major sections.

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Bokuan Li
2026-04-23 02:56:47 -04:00
parent 945bfe9946
commit 9259cd1d86
10 changed files with 149 additions and 0 deletions

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\input{./cat/index.tex}
\input{./gluing/index.tex}
\input{./tricks/index.tex}
\input{./notation/index.tex}

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\chapter{Notations}
\label{chap:notations}
\begin{tabular}{lll}
\textbf{Notation} & \textbf{Description} & \textbf{Source} \\
\hline
% ---- Category Theory ----
$\obj{\catc}$ & Objects of category $\catc$. & \autoref{definition:category} \\
$\mor{A, B}$ & Morphisms from $A$ to $B$ in a category. & \autoref{definition:category} \\
$\text{Id}_A$ & Identity morphism on $A$. & \autoref{definition:category} \\
$E \otimes F$, $x_1 \otimes \cdots \otimes x_n$ & Tensor product of modules; image of $(x_1,\ldots,x_n)$ under canonical embedding. & \autoref{definition:tensor-product} \\
$\lim_{\longrightarrow} A_i$ & Direct limit of an upward-directed system. & \autoref{definition:direct-limit} \\
$\lim_{\longleftarrow} A_i$ & Inverse limit of a downward-directed system. & \autoref{definition:inverse-limit} \\
$\mathbb{D}_n$, $\mathbb{D}$ & Dyadic rationals of level $n$; all dyadic rationals. & \autoref{definition:dyadic} \\
$\mathrm{rk}(q)$ & Dyadic rank of $q \in \mathbb{D}$. & \autoref{definition:dyadic-rank} \\
$M(x)$ & Unique $M(x) \subset \mathbb{N}^+ \cap [1, \mathrm{rk}(x)]$ such that $x = \sum_{n \in M(x)} 2^{-n}$. & \autoref{proposition:dyadic-subset}
\end{tabular}