Algebra Seminar: East -- Congruences on categories and their ideals

James East (Western Sydney University) 

Friday 11 October, 12-1pm, Place: Carslaw 375 

Title: Congruences on categories and their ideals 

Abstract: A congruence on a category is an equivalence on morphisms that respects
objects and is compatible with composition.  Congruences are used to form quotient
categories, so play the role of normal subgroups or ideals from group and ring theory.
This talk will describe joint work with Nik Ruskuc (St Andrews), in which we classify
the congruences on many well-known categories and their ideals.  Examples include
partition categories, Brauer categories, Temperley-Lieb (planar) categories and Jones
(annular) categories, as well as several categories of (linear) transformations and
braids.  These are all applications of general results concerning ideal extensions in a
certain class of stable, von Neumann regular categories.