At Ross’ 60th birthday I spoke about his complicial sets, and I propose to do so again at his 80th. On that occasion my focus was on the strict variant of this notion, whereas this time I’d like to discuss the current state of the art in the theory of their weak cousins. For most of the intervening time between Streetfests this is a topic that hasn’t been central for me. Over last two or three years, however, it is one that has reimposed itself on my consciousness largely thanks to some excellent work by Viktoria Ozornova, Martina Rovelli, our own Yuki Maehara, Felix Loubaton and others. If we have time, I will also try to say a few things about ideas I’ve been working on with Jonathan Weinberger and Emily Riehl to build type theoretic languages for expressing -category theory using complicial sets.
As we go I may pause, on occasion, to speak a little about some specific ways in which Ross’ remarkable perspective on mathematics and category theory has inspired me over the years…. Or maybe, in truth, that's all I will be talking about.😺