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 explain and explore some of the current ideas from category theory that enable various mathematical descriptions of hierarchical structures.
Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, interpreted systems , and the related Kripke semantics of the… (More)
—In this work, we investigate a new objective measurement for assessing the video playback quality for services delivered in networks that use TCP as a transport layer protocol. We define the new metric as pause intensity to characterize the quality of playback in terms of its continuity since, in the case of TCP, data packets are protected from losses but… (More)
We give an interpretation of Yetter's Invariant of manifolds M in terms of the homotopy type of the function space TOP(M, B(G)), where G is a crossed module and B(G) is its classifying space. From this formulation, there follows that Yetter's invariant depends only on the homotopy type of M , and the weak homotopy type of the crossed module G. We use this… (More)
We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more eecient, and often geometric, data. The methods utilise crossed modules and crossed resolutions.
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes.