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Ruby Khondaker (she/her) (Jul 09 2025 at 08:42):I'm trying to see how higher categories with "cubical" shapes are defined, and thought a good testing ground for these would be 2-categories - so you have 0-squares, 1-squares and 2-squares, with composition laws for them. Ideally composition of 1-squares would only be weakly associative and unital?
It seems like double bicategories might be a version of this (at least if we only take edge-symmetric ones). I'll read up on the definition, but I guess I wanted to ask - at a high-level, why are they seemingly a lot harder to define than ordinary (edge-symmetric) double categories?
Nathanael Arkor (Jul 09 2025 at 08:51):The introduction of the recent preprint by @Aaron David Fairbanks and @Mike Shulman explains this very nicely.
Ruby Khondaker (she/her) (Jul 09 2025 at 08:54):Woahhhh that’s incredibly recent!!