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.
Bacterial communities in the airways of cystic fibrosis (CF) patients are, as in other ecological niches, influenced by autogenic and allogenic factors. However, our understanding of microbial colonization in younger versus older CF airways and the association with pulmonary function is rudimentary at best. Using a phylogenetic microarray, we examine the… (More)
This is an account for the combinatorially minded reader of various categories of directed and undirected graphs, and their analogies with the category of sets. As an application, the endomorphisms of a graph are in this context not only composable, giving a monoid structure, but also have a notion of adjacency, so that the set of en-domorphisms is both a… (More)
We describe a case study of the behaviour of four agents using a space based communication architecture. We demonstrate that interoperability may be achieved by the agents merely describing information about themselves using an agreed upon common ontology. The case study consists of an exercise logger, a game, a mood rendered attached to audio player and… (More)
We obtain some explicit calculations of crossed Q-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups.
We associate to a Hausdorff space, X, a double groupoid, ρ 2 (X), the homotopy double groupoid of X. The construction is based on the geometric notion of thin square. Under the equivalence of categories between small 2-categories and double categories with connection given in [BM] the homotopy double groupoid corresponds to the homotopy 2-groupoid, G 2 (X),… (More)
The aim is to apply string-rewriting methods to compute left Kan extensions, or, equivalently , induced actions of monoids, categories, groups or groupoids. This allows rewriting methods to be applied to a greater range of situations and examples than before. The data for the rewriting is called a Kan extension presentation. The paper has its origins in… (More)
This survey article shows how the notion of \change of base", used in some applications to homotopy theory of the fundamental groupoid, has surprising higher dimensional analogues, through the use of certain higher homotopy groupoids with values in forms of multiple groupoids.
We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere.