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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.

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  • (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.

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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.

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