Andrew Brooke-Taylor, University of Leeds
Categorifying Borel reducibility
The theory of Borel reducibility has had great success in ruling out proposed classifications in various areas of mathematics. However, this framework doesn't account for an important feature of such classifications - they are often expected to be functorial, not just respecting isomorphism but taking any homomorphism between the objects in question to a homomorphism of the invariants. I will talk about some work in progress with Filippo Calderoni, extending the framework to include functoriality and noting some differences this immediately introduces from the standard framework.