Mathematics Preprints 2003
Category Theory & Homotopy Theory
03.02 : DONADZE, G., INASSARIDZE, N. & PORTER, T.
n-fold Cech derived functors and generalised Hopf type formulas
Summary:The notion of n-fold Cech derived functors is introduced and studied. This is illustrated using the n-fold Cech derived functors of the nilization functors Z_k. This gives a new purely algebraic method for the investigation of the Brown-Ellis generalised Hopf formula for the higher integral group homology and for its further generalisation. The paper ends with an application to algebraic K-theory.
Published in:K-Theory 35 (2005) 341-373.
- (the old December 2004 version) pdf file: 03_02.pdf
03.05 : BROWN, R. & PORTER, T.
Category theory and higher dimensional algebra: potential descriptive tools in neuroscience
Summary: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.
Published in:Proc. Int. Conf. on Theoretical Neurobiology, New Delhi 2003, ed. N.C. Singh, National Brain Research Centre (2003) 80-92.
- pdf file: 03_05.pdf
03.15 : BROWN, R., PATON, R. & PORTER, T.
Categorical language and hierarchical models for cell systems
Summary:The aim is to explain and explore some of the current ideas from category theory that enable various mathematical descriptions of # hierarchical structures.
Published in:Computation in Cells and Tissues - Perspectives and Tools of Thought, R. Paton, H. Bolouri, M. Holcombe, J.H. Parish, R. Tateson (eds.), Springer Series on Natural Computing (2004) 289-303.
- pdf file: 03_15.pdf