A poset-like approach to positive opetopes

TL;DR

This paper introduces a new formalisation of positive opetopes using posets to organize faces, and proves its equivalence to existing definitions by Zawadowski.

Contribution

It presents a novel poset-based formalisation of positive opetopes and establishes its equivalence with the traditional approach.

Findings

New poset-based formalisation of positive opetopes

Proof of equivalence with Zawadowski's definition

Enhanced understanding of face organisation in positive opetopes

Abstract

We introduce in this paper a new formalisation of positive opetopes where faces are organised in a poset. Then we show that our definition is equivalent to that of positives opetopes as given by Marek Zawadowski.