Seminar
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Location: | SLMath: Online/Virtual |
The Equivariant Uniform Kan Fibration Model Of Cubical Homotopy Type Theory
Zoom Link:
https://msri.zoom.us/s/93059090699
In joint work with Steve Awodey, Evan Cavallo, Thierry Coquand, and Christian Sattler, we introduce a constructive model for homotopy type theory on a category of cubical sets that defines a model category that is Quillen equivalent to spaces and supports "cellularly-inductive" constructions. This latter property is a feature of the cube category we use: the cartesian cube category, which is an Eilenberg-Zilber generalized Reedy category. Our model is a variation of ABCFHL obtained by demanding that the fibrations satisfy an additional equivariance condition on top of the uniform Kan condition. As a consequence, all quotients of cubes by groups of symmetries are contractible. Time permitting, we sketch the proof of the comparison Quillen equivalence, which makes heavy use of these contractible cube quotients.
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The Equivariant Uniform Kan Fibration Model Of Cubical Homotopy Type Theory
H.264 Video | 25038_28427_8353_The_Equivariant_Uniform_Kan_Fibration_Model_of_Cubical_Homotopy_Type_Theory.mp4 |