We introduce MTT, a dependent type theory which supports multiple modalities. MTT is
parametrized by a mode theory which specifies a collection of modes, modalities, and …

We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

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 …

We combine homotopy type theory with axiomatic cohesion, expressing the latter internally
with a version of 'adjoint logic'in which the discretization and codiscretization modalities are …

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

We report on the development of the HoTT library, a formalization of homotopy type theory in
the Coq proof assistant. It formalizes most of basic homotopy type theory, including …

Modalities are everywhere in programming and mathematics! Despite this, however, there
are still significant technical challenges in formulating a core dependent type theory with …

We present a development of the theory of higher groups, including infinity groups and
connective spectra, in homotopy type theory. An infinity group is simply the loops in a …

We define a general framework that abstracts the common features of many intuitionistic
substructural and modal logics/type theories. The framework is a sequent calculus/normal …

How do spaces in physics emerge from pregeometric discrete building blocks governed by
computational rules? To address this question we investigate non-deterministic rewriting …