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 …

This talk gave a sketch of the contents and background to a book with the titleNonabelian
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …

A 2-CATEGORIES COMPANION 1. Overview and basic examples. This paper is a rather
informal guide to some of the basic theory of 2- Page 1 A 2-CATEGORIES COMPANION …

String diagrams turn algebraic equations into topological moves that have recurring shapes,
involving the sliding of one diagram past another. We individuate, at the root of this fact, the …

This paper develops the foundations of a simplicial theory of weak ω-categories, which
builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented …

The goal of this paper is to provide the last equivalence needed in order to identify all known
models for (∞, 2) (∞,2)‐categories. We do this by showing that Verity's model of saturated 2 …

In this paper we re-develop the foundations of the category theory of quasi-categories (also
called∞-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi …

In this dissertation I prove several results which serve to relate Martin-Löf's intensional type
theory to certain structures arising in homotopy theory and higherdimensional category …

We study four types of (co) cartesian fibrations of $\infty $-bicategories over a given base
$\mathcal {B} $, and prove that they encode the four variance flavors of $\mathcal {B} …

We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is
associative and forms a left Quillen bifunctor with respect to the bicategorical model category …