The theory of quantales from a geometric perspective

07/03/2019, 14:00 - 15:00 in MAP/0G/014

Weiss, Ittay (Portsmouth)


Abstract:

A quantale is a portemanteau of ‘quantum’ and ‘locale’, a term coined by Mulvey in his study of qunatisation of topology. A quantale is a complete lattice with further algebraic structure. Usually, the morphisms of quantales are given by equalities, e.g., f(a+b)=f(a)+f(b). However, due to the ordering present, it is natural to consider weakening the requirement of additivity to sub-additivity: f(a+b) ≤ f(a)+f(b). The aim of the talk is to elucidate the differences between the two approaches, understand why one is algebraic while the latter is geometric, and to present some of the properties of quantales from the geometric perspective. The applications in mind are to topology and geometry in a broad sense.

Mathematical Sciences Research Centre