Simplicial Delta Versus Fat Delta in Higher Category Theory

Watch a 59-minute Topos Institute Colloquium lecture exploring the comparative analysis between simplicial delta and fat delta structures in higher category theory. Delve into how simplicial objects describe various categorical structures, from basic categories using Segal conditions to strict 2-categories and double categories in higher dimensions. Learn about the fat delta structure introduced by Joachim Kock and its application in defining fair 2-categories. Examine the direct comparison between fair 2-categories and weakly globular double categories, understanding how weak globularity conditions relate to weak units. Discover the intricate interplay between simplicial delta and fat delta structures, along with novel properties that emerge from their relationship. Consider the implications of these findings for potential higher-dimensional generalizations in category theory.