Univalent homotopy type theory (HoTT) may be seen as a language for the category of ∞-
groupoids. It is being developed as a new foundation for mathematics and as an internal …

Despite the plausible necessity of topological protection for realizing scalable quantum
computers, the conceptual underpinnings of topological quantum logic gates had arguably …

Homotopy type theory is a new branch of mathematics, based on a recently discovered
connection between homotopy theory and type theory, which brings new ideas into the very …

We study different formalizations of finite sets in homotopy type theory to obtain a general
definition that exhibits both the computational facilities and the proof principles expected …

Working in homotopy type theory, we provide a systematic study of homotopy limits of
diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the …

The study of homotopy theoretic phenomena in the language of type theory is sometimes
loosely calledsynthetic homotopy theory'. Homotopy theory in type theory is only one of the …

Abstract The Minimalist Foundation, MF for short, is a two-level foundation for constructive
mathematics ideated by Maietti and Sambin in 2005 and then fully formalized by Maietti in …

We investigate predicative aspects of constructive univalent foundations. By predicative and
constructive, we respectively mean that we do not assume Voevodsky's propositional …

We prove a conservativity result for extensional type theories over propositional ones, ie
dependent type theories with propositional computation rules, using insights from homotopy …

Higher inductive types (HITs) in homotopy type theory are a powerful generalization of
inductive types. Not only can they have ordinary constructors to define elements, but also …