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- Jukka Honkola, Hannu Laine, Ronald Brown, Olli Tyrkko
- ISCC
- 2010

Introduction The aim of this paper is to show one more facet of the role of crossed complexes as generalisations of both groups (or groupoids) and of chain complexes. We do this by defining and establishing the main properties of a classifying space functor B: mia-> SToft from the category of crossed complexes to the category of spaces. The basic example of… (More)

- Fahd Ali Al-Agl, Ronald Brown, Richard Steiner
- 2000

We show the equivalence of two kinds of strict multiple category, namely the well-known globular o-categories, and the cubical o-categories with connections. # 2002 Elsevier Science (USA)

A generalised tensor product G 0 H of groups G, H has been introduced by R. Brown and J.-L. Loday in [3,4]. It arises in applications in homotopy theory of a generalised Van Kampen theorem. The reason why G 0 H does not necessarily reduce to GUh Oz Huh, the usual tensor product over Z of the abelianisations, is that it is assumed that G acts on H (on the… (More)

- Ronald Brown
- 2004

This is an extended account of a short presentation with this title given at the Min-neapolis IMA Workshop on 'n

- RONALD BROWN, GHAFAR H. MOSA, Ghafar H. Mosa
- 1999

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 also given of the theorem of Spencer, that the category of small 2-categories is equivalent to the category of edge symmetric double categories with thin structure.

- RONALD BROWN
- 1988

In this note we generalise Hopfs formula for the second homology of a group G in terms of a free presentation R >-• F^» G. We prove: THEOREM 1. Let R lt ...,R n be normal subgroups of a group F such that F/Y\i iiin Ri = G, and for each proper subset A of <«> = {1,...,«} the groups H r (F/Y[ ieA R,) are trivial for r = 2ifA = 0, and for r = \A\ + 1 and \A\ +… (More)

This work is devoted to an interpretation and computation of the first homology groups of the small category given by a rewriting system. It is shown that the elements of the first homology group may be regarded as the equivalence classes of the flows in a graph of the rewriting system. This is applied to calculating the homology groups of asynchronous… (More)