Approximate Fibrations in Higher Topos Theory

Fuente: arXiv
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Main Authors: Kremer, Christian, Volpe, Marco
Format: Preprint
Published: 2025
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author Kremer, Christian
Volpe, Marco
author_facet Kremer, Christian
Volpe, Marco
contents The goal of this paper is to put the theory of approximate fibrations into the framework of higher topos theory. We define the notion of an approximate fibration for a general geometric morphism of $\infty$-topoi, give several characterizations in terms of shape theory and compare it to the original definition for maps of topological spaces of Coram and Duvall. Furthermore, we revisit the notion of cell-like maps between topoi, and generalize Lurie's shape-theoretic characterization by giving a purely topos-theoretical proof.
format Preprint
id arxiv_https___arxiv_org_abs_2510_24629
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Approximate Fibrations in Higher Topos Theory
Kremer, Christian
Volpe, Marco
Geometric Topology
Algebraic Topology
Category Theory
The goal of this paper is to put the theory of approximate fibrations into the framework of higher topos theory. We define the notion of an approximate fibration for a general geometric morphism of $\infty$-topoi, give several characterizations in terms of shape theory and compare it to the original definition for maps of topological spaces of Coram and Duvall. Furthermore, we revisit the notion of cell-like maps between topoi, and generalize Lurie's shape-theoretic characterization by giving a purely topos-theoretical proof.
title Approximate Fibrations in Higher Topos Theory
topic Geometric Topology
Algebraic Topology
Category Theory
url https://arxiv.org/abs/2510.24629