Two equivalent descriptions of opetopes: in terms of zoom complexes and of partial orders

TL;DR

This paper presents two equivalent frameworks for describing opetopes, one using posets and the other using constellations, establishing their formal equivalence.

Contribution

It introduces a new poset-based definition of opetopes and proves its equivalence to the existing constellation-based description.

Findings

Poset-based definition of opetopes introduced.

Equivalence between poset and constellation descriptions established.

Provides a new perspective on the structure of opetopes.

Abstract

We introduce in this paper a definition of (non necessarily positive) opetopes where faces are organised in a poset. Then we show that this description is equivalent to that given in terms of constellations by Kock, Joyal, Batanin and Mascari.