A cubical model for weak omega-categories

Yuki Maehara – 3 June 2020

In this joint project with Tim Campion and Chris Kapulkin, we propose a cubical version of complicial sets as another model for weak omega-categories. I will start the talk by recalling the globular and cubical approaches to strict omega-categories and Steiner's characterisation of their (marked) cubical nerves. Then I will present our model and the lax and pseudo Gray tensor products in this setting. I will also discuss how this model relates to the original complicial sets.