The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as
defined by Drinfeld in quantum group theory, has a topological interpretation as a group of …

This book provides an introduction to modern homotopy theory through the lens of higher
categories after Joyal and Lurie, giving access to methods used at the forefront of research …

The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-
equivalences. Our main result is a description of the map** spaces between two dg …

In this paper we establish a universal characterization of higher algebraic K–theory in the
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …

A Historical background....................................... xi A. 1 The conjectural theory described by
Beilinson............ xi A. 2 Voevodsky's motivic complexes........................ xii A. 3 Morel and …

We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in
homotopical and higher categorical contexts. In this first part we investigate a notion of …

qrothendie k introduit d ns À la poursuite des champs l notion de catégorie testD petite
tégorie y nt pr définition l propriété que les préf isE e ux sur elleE i sont n turellement des …

Begin with a small category C. The goal of this short note is to point out that there is such a
thing as a “universal model category built from C.” We describe applications of this to the …

We verify the existence of left Bousfield localizations and of enriched left Bousfield
localizations, and we prove a collection of useful technical results characterizing certain …