The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

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

Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …

This textbook is an introduction to the theory of infinity-categories, a tool used in many
aspects of modern pure mathematics. It treats the basics of the theory and supplies all the …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

We construct the\'etale motivic Borel-Moore homology of derived Artin stacks. Using a
derived version of the intrinsic normal cone, we construct fundamental classes of quasi …

This paper is the first in a series in which we offer a new framework for hermitian K-theory in
the realm of stable∞-categories. Our perspective yields solutions to a variety of classical …

This text is an introduction to topos theory. Our purpose is to sketch some of the intuitive
ideas underlying the theory, not to give a systematic exposition of it. It may serve as a …

In this book we prove (Thm. 4. 3.24) unified classification results for stable equivariant Γ-
principal bundles when the underlying homotopy type SΓ of the topological structure group Γ …

Yoneda's lemma for internal higher categories Page 1 YONEDA’S LEMMA FOR INTERNAL
HIGHER CATEGORIES LOUIS MARTINI Abstract. We develop some basic concepts in the theory …