approx-diff/notes.tex at main · bobatkey/approx-diff · GitHub

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\documentclass[acmsmall,screen]{acmart}

\usepackage{tabularx}
\usepackage{bbm}
\usepackage{bbold}
\usepackage{mathpartir}
\usepackage{subcaption}
\usepackage{tikz-cd}
\usepackage{xspace}

%\geometry{paperwidth=8.3in, paperheight=11.7in} % force to A4 for now
\settopmatter{printacmref=false}
\citestyle{acmauthoryear}
\raggedbottom

\input{macros}

\begin{document}

\title{Approximation as Differentiation: Notes}

\maketitle

\section{Overview}

Covered here:
\begin{itemize}
\item automatic differentiation (\secref{auto-diff})
\item stable functions (\secref{stable-functions})
\item $\CMon$, the category of commutative monoids (\secref{cmon})
\item $\CMon$-enrichment, including enriched functors and enriched Yoneda embedding (\secref{cmon-enriched})
\item biproducts and semi-additive categories (\secref{biproduct})
\item useful semi-additive categories (\secref{useful-semi-additive-categories}):
   \begin{itemize}
   \item category $\LatGal$ of bounded lattices and Galois connections (\secref{categories-with-biproducts:latgal})
   \item category $\LatConj$ of bounded distributive lattices and conjugate pairs
   (\secref{categories-with-biproducts:latconj})
   \item category $\FinVect_F$ of finite-dimensional vector spaces over a field $F$
   (\secref{categories-with-biproducts:fdvect})
   \end{itemize}
\item category $\Fam(I,\cat{C})$ of $I$-indexed families of objects of $\cat{C}$ (\secref{fam})
\item set-indexed products (\secref{set-indexed-product})
\item Grothendieck construction $\Grothendieck{\cat{C}}F$ and category of families $\Fam(\cat{C})$
(\secref{grothendieck})
\item useful categories of families for automatic approximation
(\secref{galois-slicing-auto-diff-via-fam}):
   \begin{itemize}
      \item Galois slicing via $\Fam(\LatGal)$ (\secref{galois-slicing-auto-diff-via-fam:galois-slicing})
      \item automatic differentiation via $\Fam(\FinVect)$ (\secref{galois-slicing-auto-diff-via-fam:auto-diff})
   \end{itemize}
\item matrices over a commutative semiring; $\Mat(\Two)$ as worked example (\secref{matrix})
\item stable coproducts (\secref{stable-coproducts})
\item predicate systems (\secref{predicate-system})
\end{itemize}

\noindent $\Set$ will usually be $\Setoid$ in the Agda implementation but we will gloss that detail for now.

\input{notes/preliminaries}
\input{notes/auto-diff}
\input{notes/stability}
\input{notes/cmon}
\input{notes/cmon-enriched}
\input{notes/biproduct}
\input{notes/useful-semi-additive-categories}
\input{notes/fam}
\input{notes/set-indexed-product}
\input{notes/grothendieck}
\input{notes/auto-diff-galois-slicing-via-fam}
\input{notes/matrix}
\input{notes/stable-coproducts}
\input{notes/predicate-system}

\bibliographystyle{ACM-Reference-Format}
\bibliography{bib}

\end{document}