Tags:degrees of relatedness, internal language, parametricity, presheaf models and two-level type theory
Abstract:
Main result (proof WIP): The type system for Degrees of Relatedness (a multimode system with modalities for parametricity, irrelevance and more) is (under conditions) the internal language of a lax-idempotent 2-monad (such as PSh, modulo strictification) iteratively applied to a single category. In particular, it can be seen as a modal system for multilevel type theory.
Lax-Idempotent 2-Monads, Degrees of Relatedness, and Multilevel Type Theory