DeepAI AI Chat
Log In Sign Up

On the Formalization of Higher Inductive Types and Synthetic Homotopy Theory

08/31/2018
by   Floris van Doorn, et al.
0

The goal of this dissertation is to present synthetic homotopy theory in the setting of homotopy type theory. We will present various results in this framework, most notably the construction of the Atiyah-Hirzebruch and Serre spectral sequences for cohomology, which have been fully formalized in the Lean proof assistant.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/04/2021

Synthetic fibered (∞,1)-category theory

We study cocartesian fibrations in the setting of the synthetic (∞,1)-ca...
06/22/2018

Cubical informal type theory: the higher groupoid structure

Following a project of developing conventions and notations for informal...
02/08/2018

Impredicative Encodings of (Higher) Inductive Types

Postulating an impredicative universe in dependent type theory allows Sy...
01/11/2023

Patch Locale of a Spectral Locale in Univalent Type Theory

Stone locales together with continuous maps form a coreflective subcateg...
10/04/2019

Construction of the Circle in UniMath

We show that the type TZ of Z-torsors has the dependent universal proper...
02/26/2022

A Synthetic Perspective on (∞,1)-Category Theory: Fibrational and Semantic Aspects

Reasoning about weak higher categorical structures constitutes a challen...
12/28/2021

A Cartesian Bicategory of Polynomial Functors in Homotopy Type Theory

Polynomial functors are a categorical generalization of the usual notion...