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Mathematics > Algebraic Topology

arXiv:2406.18497 (math)
[Submitted on 26 Jun 2024]

Title:The equivariant model structure on cartesian cubical sets

Authors:Steve Awodey, Evan Cavallo, Thierry Coquand, Emily Riehl, Christian Sattler
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Abstract: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.
Subjects: Algebraic Topology (math.AT); Logic in Computer Science (cs.LO); Logic (math.LO)
Cite as: arXiv:2406.18497 [math.AT]
  (or arXiv:2406.18497v1 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.2406.18497

Submission history

From: Evan Cavallo [view email]
[v1] Wed, 26 Jun 2024 17:00:33 UTC (97 KB)
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