Dear all, Taichi Uemura will give a talk for the second session of the PCT seminar (https://pctseminar.github.io/) on Friday January 16 at 10am JST/12pm AED (1am UTC). The zoom link to join the seminar is here: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS... Title: A direct-categorical approach to opetopic sets and opetopes Abstract: Opetopes and opetopic sets were introduced by Baez and Dolan as a combinatorial approach to weak ω-categories. Since its birth, several equivalent definitions have been proposed. Recently, Leclerc gave a posetal definition of opetopes, where an opetope is encoded as a poset of cells ordered by the subcell relation. This seems to be the most elementary and simple definition of opetopes, but there is some complication related to loops. In this talk, I propose another elementary definition of opetopes, encoding an opetope as a direct category rather than a poset. Loop issues are resolved by allowing distinct parallel morphisms, and the theory of opetopic sets gets simplified. We hope to see you there! Best wishes, Soichiro Fujii, Zeinab Galal and JS PL