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 …

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 …

A slowly-growing number of computer scientists have found that ideas from topology can be
used to analyze and understand problems in distributed computing. In this paper, we review …

The main result is that two possible structures which may be imposed on an edge symmetric
double category, namely a connection pair and a thin structure, are equivalent. A full proof is …

A more explicit form of this definition is given in Definition 2.1. The concept was originated by
Brown and Higgins in [5], in connection with homotopy theory. Their definition did not …

As an example of the categorical apparatus of pseudo algebras over 2-theories, we show
that pseudo algebras over the 2-theory of categories can be viewed as pseudo double …

If X is a Hausdorff space we construct a 2-groupoid G 2 X with the following properties. The
underlying category of G 2 X is thepath groupoid" of X whose objects are the points of X and …

The strict globular ω-categories formalize the execution paths of a parallel automaton and
the homotopies between them. One associates to such (and any) ω-category [Cscr] three …

We outline the main features of the definitions and applications of crossed complexes and
cubical $\omega $-groupoids with connections. These give forms of higher homotopy …

The relationships between thin elements, commutative shells and connections in cubical
omega-categories are explored by a method which does not involve the use of pasting …