An elementary definition of opetopic sets

Abstract

We propose elementary definitions of opetopes and opetopic sets. We directly define opetopic sets by a simple structure and several axioms. Opetopes are then opetopic sets satisfying one more axiom. We show that our definition is equivalent to the polynomial monad definition given by Kock, Joyal, Batanin, and Mascari. We also show that our category of opetopes is equivalent to the one given by Ho Thanh.