Duality for positive opetopes and positive zoom complexes

TL;DR

This paper establishes a duality between positive zoom complexes and positive opetopes, extending the duality to opetopic cardinals, thereby deepening the understanding of their categorical relationships.

Contribution

It introduces a duality framework connecting positive zoom complexes and positive opetopes, and extends this duality to opetopic cardinals.

Findings

Positive zoom complexes form a dual category to positive opetopes.

The duality extends to opetopic cardinals.

The duality is established with natural morphisms.

Abstract

We show that the positive zoom complexes, with fairly natural morphisms, form a dual category to the category of positive opetopes with contraction epimorphisms. We also show how this duality can be extended to opetopic cardinals.