\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} \\
    $[n]$ & $\bracs{1, \cdots, n}$ & N/A
\end{tabular}