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arXiv · 2406.18497

The equivariant model structure on cartesian cubical sets

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.

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Steve Awodey, Evan Cavallo, Thierry Coquand, Emily Riehl, Christian Sattler. 2024-06-26. The equivariant model structure on cartesian cubical sets. https://doi.org/10.1016/j.aim.2026.110965

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