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 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 …

Quasi-categories vs Segal spaces Page 1 Contemporary Mathematics Volume 431, 2007
Quasi-categories vs Segal spaces Andre Joyal and Myles Tierney To Ross Street on the …

We use hypercovers to study the homotopy theory of simplicial presheaves. The main result
says that model structures for simplicial presheaves involving local weak equivalences can …

We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

In this work we present a new approach to the theory of noncommutative motives and use it
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …

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 …

We show that every combinatorial model category is Quillen equivalent to a localization of a
diagram category (where “diagram category” means diagrams of simplicial sets). This says …

We propose a notion of weak (n+ k, n)–category, which we call (n+ k, n)–Θ–spaces. The (n+
k, n)–Θ–spaces are precisely the fibrant objects of a certain model category structure on the …

We show that if U* is a hypercover of a topological space X then the natural map hocolim
U*→ X is a weak equivalence. This fact is used to construct topological realization functors …