University of Sydney Algebra Seminar

James East (Western Sydney University)

Friday 6 September, 12-1pm, Place: Carslaw 375

Congruences on categories and their ideals

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.