From the 1 of 4 linked papers with an AI index.
4 papers
Extension Types for Free
Nicolai Kraus
The paper shows how extension types, which appear in various dependent type theories, can be uniformly defined within two‑level type theory without adding new axioms, making the co…
Generalized Decidability via Brouwer Trees
Tom de Jong, Nicolai Kraus, Aref Mohammadzadeh +1
In the setting of constructive mathematics, we suggest and study a framework for decidability of properties, which allows for finer distinctions than just "decidable, semidecidable…
A study of Kock's fat Delta
Tom de Jong, Nicolai Kraus, Simona Paoli +1
Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock and pro…
The Leibniz adjunction in homotopy type theory, with an application to simplicial type theory
Tom de Jong, Nicolai Kraus, Axel Ljungström
Simplicial type theory extends homotopy type theory and equips types with a notion of directed morphisms. A Segal type is defined to be a type in which these directed morphisms can…