All Outputs (3)

Epimorphisms and acyclic types in univalent foundations (2024)
Journal Article
Buchholtz, U., De Jong, T., & Rijke, E. (in press). Epimorphisms and acyclic types in univalent foundations. Journal of Symbolic Logic,

We characterize the epimorphisms in homotopy type theory (HoTT) as the fiberwise acyclic maps and develop a type-theoretic treatment of acyclic maps and types in the context of synthetic homotopy theory as developed in univalent foundations. We prese... Read More about Epimorphisms and acyclic types in univalent foundations.

Apartness, sharp elements, and the Scott topology of domains (2023)
Journal Article
de Jong, T. (2023). Apartness, sharp elements, and the Scott topology of domains. Mathematical Structures in Computer Science, 33(7), 573-604. https://doi.org/10.1017/S0960129523000282

Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of being unequal,... Read More about Apartness, sharp elements, and the Scott topology of domains.

On Small Types in Univalent Foundations (2023)
Journal Article
de Jong, T., & Escardó, M. H. (2023). On Small Types in Univalent Foundations. Logical Methods in Computer Science, 19(2), 8:1-8:33. https://doi.org/10.46298/LMCS-19%282%3A8%292023

We investigate predicative aspects of constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky’s propositional resizing axioms or excluded middle. Our work complements existing work on... Read More about On Small Types in Univalent Foundations.