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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.CT2025
Synthetic perspectives on spaces and categories
Emily Riehl
Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a nativel…