Higher-dimensional category theory is the study of n-categories, operads, braided monoidal
categories, and other such exotic structures. It draws its inspiration from areas as diverse as …

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 …

Dimension three is an important test-bed for hypotheses in higher category theory and
occupies something of a unique position in the categorical landscape. At the heart of matters …

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 …

arXiv:math/0107188v1 [math.CT] 25 Jul 2001 Page 1 arXiv:math/0107188v1 [math.CT] 25 Jul
2001 A Survey of Definitions of n-Category Tom Leinster Department of Pure Mathematics …

The notion of quasi-category was introduced by Boardman and Vogt in their work on
homotopy invariant algebraic structures [BV]. A Kan complex and the nerve of a category are …

We axiomatise the theory of $(\infty, n) $-categories. We prove that the space of theories of
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …

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 is the first in a series of papers devoted to the theory of decomposition spaces, a
general framework for incidence algebras and Möbius inversion, where algebraic identities …

The study of higher categories is attracting growing interest for its many applications in
topology, algebraic geometry, mathematical physics and category theory. In this highly …