Categorifying Turbulence in Borel Reducibility

The framework of Borel reducibility allows us to compare the complexity of a variety of different mathematical problems. It has had much success in showing that certain classification programmes (in different areas of mathematics) were impossible tasks, using Hjorth's notion of turbulence as a central tool. However, the Borel reducibility framework has previously ignored an important feature of most classification programmes, known as functoriality.

The aim of this project is to find a functorial version of turbulence. In the longer term, this could be used to show that more classification programmes are impossible to complete.