Categorifying Borel reducibility

Abstract: Borel reducibility is a framework that has been very successful in showing that classification programmes in different areas of mathematics are not possible to complete. However, a feature of many such classification programmes that is not accounted for in the standard Borel reducibility framework is functoriality - a good classification function is expected to respect all maps between objects, not just the isomorphisms. I will present an extension of the Borel reducibility framework that takes functoriality into account, and give some initial results showing that this is a meaningful refinement of the standard framework.

logic

Audience: researchers in the topic

Barcelona Set Theory Seminar

Series comments: To attend please send a request to bagaria@ub.edu and we'll send you the link.