Accessible higher modalities

Abstract

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Carles Casacuberta[en] The main goal of this master’s thesis is to study localizations in the setting of homotopy type theory. In particular the special case of modalities, an object resembling the namesake notion in classical logic that allows to qualify statements to express things as possibility or necessity. In the first chapter we introduce the syntax of homotopy type theory and some motivating examples for the study of modalities. Next, we study localizations and modalities as described in [1; 2]. We focus on the fact that accessible modalities correspond to nullifications and work on the existence of non-accessible modalities. Finally we explore the use of Agda (a programming language for automatic proof verification) towards implementing results about factorization systems and modalities