Categorifying Borel reducibility

Andrew Brooke-Taylor, University of Leeds. Part of the proofs, constructions and computations seminar series.

Borel reducibility has been very successfully applied to questions in various different areas of mathematics. One way in which it falls short, however, is that it doesn't consider morphisms, whereas morphisms are a natural feature of many of these application areas. Also, predating the interest in Borel reducibility, a lot of work was done on universal categories, with similar aims and constructions but without the Borel perspective. I will talk about joint work in progress with Filippo Calderoni (Muenster) aiming to bring these topics together.