Pure Maths Colloquium: The intuitions of higher order categories and groupoids for the study of local-to-global problems
5 June 2006 00:00 in CM221
"I will give some of the intuitions which have fostered a collaboration with Philip Higgins since the 1970s, and with others, and which have suggested new foundations for basic homotopy theory. The aim is to have algebra which models the geometry and *because of this* allows new calculations, sometimes needing computer implementation. A slogan for this approach to local-to-global problems is `algebraic inverses to subdivision'. Pursuing this idea reveals a range of new algebraic structures which, under the term `higher dimensional algebra', are used by workers in mathematics, physics, computer science, and have potential in biology. Such algebra arises from sets of partial operations whose domains are defined by geometric conditions. "
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