One Citation
Left-exact Localizations of $\infty$-Topoi II: Grothendieck Topologies
- Mathematics
- 2022
This paper continues our study of left-exact localizations of ∞-topoi. We revisit the work of Toën– Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and…
References
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Localization in Homotopy Type Theory
- Mathematics
- 2018
We study localization at a prime in homotopy type theory, using self maps of the circle. Our main result is that for a pointed, simply connected type $X$, the natural map $X \to X_{(p)}$ induces…
Modalities in homotopy type theory
- MathematicsLog. Methods Comput. Sci.
- 2020
The theory of factorization systems, reflective subuniverses, and modalities in homotopy type theory, including their construction using a "localization" higher inductive type, are developed.
Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy
- Philosophy
- 2020
For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate…
Formalizing Cartan Geometry in Modal Homotopy Type Theory
- Mathematics
- 2017
Both, the category of smooth manifolds and the category of schemes may be faithfully embedded in categories of (higher) sheaves on appropriate sites. Homotopy Type Theory is used to reason about…
Good Fibrations through the Modal Prism
- Mathematics
- 2019
Homotopy type theory is a formal language for doing abstract homotopy theory --- the study of identifications. But in unmodified homotopy type theory, there is no way to say that these…
Semantics of higher inductive types
- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2019
Abstract Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very…
Brouwer's fixed-point theorem in real-cohesive homotopy type theory
- MathematicsMathematical Structures in Computer Science
- 2017
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…
A generalized Blakers–Massey theorem
- MathematicsJournal of Topology
- 2020
We prove a generalization of the classical connectivity theorem of Blakers–Massey, valid in an arbitrary higher topos and with respect to an arbitrary modality, that is, a factorization system (L,R)…