categories 1homotopy type theory 1induction principles 1simplicial type theory 1spaces 1univalence 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.CT2026
Synthetic perspectives on spaces and categories
Emily Riehl
The paper surveys proof techniques from homotopy type theory and simplicial type theory, focusing on induction over paths or arrows and constructions of (directed) univalent univer…
math.CT2026
Directed univalence for simplicial objects in an -topos
Evan Cavallo, Emily Riehl, Christian Sattler
A fundamental component of homotopy type theory, a synthetic theory of -groupoids, is Voevodsky's univalence axiom. Univalence characterizes the identity types in the unive…
math.AT2026
The equivariant model structure on cartesian cubical sets
Steve Awodey, Evan Cavallo, Thierry Coquand +2
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…