Modal homotopy type theory

Geometric HoTT and comonadic modalities - Sandiego

Geometry in Modal Homotopy Type Theory workshop. Carnegie Mellon University. March 11, 2019. Page 2. Outline. 1 Cohesion. 2 Geometric type theory.

Fibrational Modal Type Theory - ScienceDirect.com

There seems to be renewed interest in the notion of constructive modal type theory (and in notions of linear type theory), in part because of ...

Directed univalence in simplicial homotopy type theory

We contribute TT. , a modal extension of simplicial type theory, and use it to construct a directed univalent universe of groupoids S. In so doing, we construct ...

Formalizing Cartan Geometry in Modal Homotopy Type Theory

Both, the category of smooth manifolds and the category of schemes may be faithfully embedded in categories of (higher) sheaves on appropriate sites.

Synthetic G-Jet-Structures in Modal Homotopy Type Theory

This article constructs the moduli stack of torsion-free G-jet-structures in homotopy type theory with one monadic modality. This yields a ...

Research - Colin Zwanziger

At Natural Language and Computer Science 2018, I discussed an approach to hyperintensional Montague semantics based on modal homotopy type theory (extended ...

Abstracts - HoTT and Philosophy - WordPress.com

We add axioms to homotopy type theory to ensure the existence of such a modal operator and refer to the types of this theory as differentially cohesive types.

Multimodal Dependent Type Theory - Lirias

Then, we will take a. 'modal cut' rule, which will allow the substitution of modal terms for modal variables, to be our modal elimination rule.

Overview of Homotopy Type Theory and the Univalent Foundations ...

Open modal dialog. Why Log In? ×. Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access ...

Modal dependent type theory and dependent right adjoints

We extend the syntax and semantics with universes. Keywords: Dependent type theory; modal logic; category theory. 1. Introduction. Dependent types are a ...

Bas Spitters: Modal Dependent Type Theory and the Cubical Model

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In recent years we ...

Cartan Geometry in Modal Homotopy Type Theory - Papers With Code

This article constructs the moduli stack of torsionfree G -structures in homotopy type theory with one monadic modality.

A Fibrational Framework for Substructural and Modal Logics - DROPS

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

Stable homotopy type theory? - hopf algebras - MathOverflow

This talk describes an extension of HoTT with linear tensor and hom type formers, as a kind of 'binary modality' and its right adjoint.

Philosophy of Mathematics Seminar (Monday - Week 2, HT21)

In this talk I shall explain how modal homotopy type theory can usefully be ... types, dependent types, homotopy types, and modal types. For the ...

One reason (among many) to like Homotopy Type Theory - New APPS

Where does homotopy type theory come in? As Steve explained in his talk (and as described in the HoTT book right at the beginning, p. 3), ...

Modal HoTT on the Web. On Dependent Sums and Products - Medium

During the conversation Odersky mentioned that there was a new foundational mathematics called Homotopy Type Theory (HoTT). That really struck ...

Graded Modal Dependent Type Theory (ESOP 2021) - YouTube

Our ESOP 2021 talk on "Graded Modal Dependent Type Theory" introducing our paper https://arxiv.org/abs/2010.13163.

Literature for categories and modal logic : r/math - Reddit

There's a lot of stuff on modal logic in homotopy type theory, which is of course closely related. The papers where they build models might ...

Homotopy Theory in Homotopy Type Theory: Introduction

Many of us working on homotopy type theory believe that it will be a better framework for doing math, and in particular computer-checked ...