Corpus ID: 202889085

# Koszul Duality in Higher Topoi

@article{Beardsley2019KoszulDI,
title={Koszul Duality in Higher Topoi},
author={Jonathan Beardsley and Maximilien P'eroux},
journal={arXiv: Algebraic Topology},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Algebraic Topology
• We show that for any pointed and $k$-connective object $X$ of an $n$-topos $\mathcal{X}$ for $0\leq n\leq\infty$ and $k>0$, there is an equivalence between the $\infty$-category of modules in $\mathcal{X}$ over the associative algebra $\Omega^{k} X$, and the $\infty$-category of comodules in $\mathcal{X}$ for the cocommutative coalgebra $\Omega^{k-1}X$. Along the way, we also show that Lurie's straightening-unstraightening equivalence holds over an $(n-1)$-groupoid in any $n$-topos for \$0\leq n… CONTINUE READING