Towards higher formal category theoryMPIM

by Nathanael Arkor (Tallinn University of Technology)

Tuesday Nov 18, 2025, 11:00 AM → 12:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract Homotopy Theory Seminar

Formal category theory is a synthetic, axiomatic approach to category theory that abstracts the essential features of different flavours of category theory, including enriched category theory, internal category theory, monoidal category theory, and so on. A notable aspect of formal category theory is that it is fundamentally double category theoretic (and not, for instance, bicategory theoretic). To compare different formal category theories, the question therefore arises as into what structure double categories assemble. In contrast to the situation for n-categories, which are known to naturally assemble into (n + 1)-categories, the situation for n-tuple categories has been little studied. I will discuss this problem, explain why it is more subtle than it might at first appear, and give an answer when n <= 2, concluding by presenting a conjecture regarding general n.

This talk is based on joint work with James Deikun and Keisuke Hoshino.