The equivariant model structure on cartesian cubical sets
Artikel i vetenskaplig tidskrift, 2026
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.
Författare
Steve Awodey
Carnegie Mellon University (CMU)
Evan Cavallo
Chalmers, Data- och informationsteknik, Computing Science
Göteborgs universitet
Thierry Coquand
Göteborgs universitet
Chalmers, Data- och informationsteknik, Computing Science
Emily Riehl
Johns Hopkins University
Christian Sattler
Göteborgs universitet
Chalmers, Data- och informationsteknik, Computing Science
Advances in Mathematics
0001-8708 (ISSN) 1090-2082 (eISSN)
Vol. 495 110965Ämneskategorier (SSIF 2025)
Algebra och logik
DOI
10.1016/j.aim.2026.110965