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paper: double-spacing, declare competing interests
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artagnon committed Jan 7, 2024
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% and { ... } if in mask
\newcommandx*{\eqnarg}[3]{\ifinmask[bonak]{#1}[#2]{\{#2:#3\}}{(#2:#3)}}

% Double-spacing
\linespread{2}

\begin{document}
\title{A parametricity-based formalization of semi-simplicial and semi-cubical sets}
\begin{authgrp}
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\begin{abstract}
Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of $n$-simplices or $n$-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call \emph{indexed}. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.
\end{abstract}
\footnotetext{Competing interests: The authors declare none}
\maketitle
\vspace{-2em} % Remove space after abstract

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