The equivariant model structure on cartesian cubical sets
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913046472949760 |
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| author | Awodey, Steve Cavallo, Evan Coquand, Thierry Riehl, Emily Sattler, Christian |
| author_facet | Awodey, Steve Cavallo, Evan Coquand, Thierry Riehl, Emily Sattler, Christian |
| contents | We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber category. The key innovation is an additional equivariance condition in the specification of the cubical Kan fibrations, which can be described as the pullback of an interval-based class of uniform fibrations in the category of symmetric sequences of cubical sets. The main technical results in the development of our model have been formalized in a computer proof assistant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The equivariant model structure on cartesian cubical sets Awodey, Steve Cavallo, Evan Coquand, Thierry Riehl, Emily Sattler, Christian Algebraic Topology Logic in Computer Science Logic We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber category. The key innovation is an additional equivariance condition in the specification of the cubical Kan fibrations, which can be described as the pullback of an interval-based class of uniform fibrations in the category of symmetric sequences of cubical sets. The main technical results in the development of our model have been formalized in a computer proof assistant. |
| title | The equivariant model structure on cartesian cubical sets |
| topic | Algebraic Topology Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2406.18497 |