The diagrammatic model of (∞,n)-categoriesMPIM

by Clémence Chanavat (Tallinn University of Technology)

Tuesday Feb 3, 2026, 11:00 AM → 12:30 PM Europe/Berlin

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

Abstract Homotopy Theory Seminar

In 2020, Hadzihasanovic proposed a program that revisits Kapranov and Voevodsky's diagrammatic sets as the basis of a model of (∞,n)-categories.

Its development in the past two years have reached some milestones, including: various Quillen model structures (presenting the (∞,n)-categories and two flavors of (∞, ω)-categories), the homotopy hypothesis, a semi-strictification result, definition of Gray products and joins, and a presentation of the associated "stricter" (0, ω)-categories. 

In this talk, I will describe the diagrammatic model and overview some of these results.
I will conclude with thoughts and conjectures that could settle the question of comparing the standard and the diagrammatic models of (∞,n)-categories.

This talk is partly based on joint work with Amar Hadzihasanovic.