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 …

Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac
Lane. It describes relationships between mathematical structures. Outside of pure …

Categorical orthodoxy has it that collections of ordinary mathematical structures such as
groups, rings, or spaces, form categories (such as the category of groups); collections of 1 …

arXiv:math/9810017v1 [math.CT] 4 Oct 1998 Page 1 arXiv:math/9810017v1 [math.CT] 4 Oct
1998 Basic Bicategories Tom Leinster Department of Pure Mathematics, University of …

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 …

Page 1 |MEMOIRS Of the American Mathematical Society Number 558 Coherence for
Tricategories R. GOrdon AJ POWer ROSS Street September 1995 • Volume ll 7 • Number 558 …

The development of category theory has posed problems for the set theoretic foundations of
Mathematics. These problems arise in the use of collections such as the category of all sets …

arXiv:math/0007009v3 [math.CT] 17 Dec 2001 Page 1 arXiv:math/0007009v3 [math.CT] 17
Dec 2001 Multiple categories: the equivalence of a globular and a cubical approach Fahd …

The purpose of this review is to serve as a common introduction to the authors' papers in this
volume, by collecting together some basic notions needed by each of us, and establishing …

The purpose of this dissertation is to set up a theory of generalized operads and
multicategories, and to use it as a language in which to propose a definition of weak n …