Approximate Fibrations in Higher Topos Theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918176101498880 |
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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 |
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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 |