Category Theory and Homotopy Theory

Personnel:

Collaborators:

Prof Heiner Kamps
Prof George Janelidze (Georgia)
Dr Manuela Sobral (Coimbra)
Dr Manuel Bullejos
Prof Tony Bak (Bielefeld)
Dr Gabriel Minian (Max Planck, Bonn)

Introduction:

Category theory was introduced in 1947 to give a richer language than that of set theory, which would be better able to express the structures of homotopy and homology theory then being revealed in the work of Cartan, Eilenberg, Mac Lane, Whitehead and others. In addition to the objects in a category (corresponding to the elements in a set), one also has arrows or "morphisms" between them. Thus for instance the collection of all sets and functions between them forms a category, the category of sets.

This language and theory was soon found to have great usefulness in other branches of pure mathematics such as algebra, algebraic geometry, logic and more recently in computer science.

The basic areas of research in category theory at Bangor are directed towards achieving a greater understanding of the categorical structure and interrelationships between the various objects studied by algebraic topology and homological algebra. Recent work in these areas has resulted in a large group of fascinating new structures. These have not yet revealed all their categorical structure nor have all the potential applications of these objects been fully investigated.

Current Projects:

INTAS grant: Algebraic homotopy, Galois theory and Descent
(joint with Coimbra, Portugal and the Georgian Academy of Sciences)
Treaty of Windsor Grant: Descent Theory and its Higher Dimensional Analogues

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Latest modification to this page: 02/10/08

University of Wales, Bangor - Department of Mathematics