2015-11-18: Bram Westerbaan (Nijmegen)

Sat, 21 Oct 2023 21:24:08 +0100

Bram Westerbaan (Nijmegen)

The categorical structure of von Neumann algebras

Abstract

I would like to speak about the categorical structure of the category of von Neumann algebras, with as morphisms normal, completely positive, unital linear maps. For some years my colleagues and I have worked on identifying basic structures in this category, and while surprisingly many things do not exist or do not work in this category (it's not a topos or even an extensive category, there's no epi-mono factorisation system, there is no dagger, colimits — if they exist at all — are horrendous...), we did find some structure (the products behave reasonable in some sense, there is a 'quotient', and 'comprehension', and we have a universal property for the minimal Stinespring dilation, and a universal property for M_2—the qubit). There is no deep category theory involved by any standards, and I promise I will spare you the functional analysis, so it should be a light talk.

2015-11-18 11:00:00 UTC
LT1310