Multitopes are the same as principal ordered face structures

TL;DR

This paper establishes an equivalence between principal ordered face structures and multitopes, introducing a graded tensor theory to connect with recent nerve construction work by Leinster and Weber.

Contribution

It demonstrates the categorical equivalence between principal ordered face structures and multitopes, and introduces a graded tensor theory framework.

Findings

Category of principal ordered face structures is equivalent to multitopes

Introduces graded tensor theory for ordered face structures

Connects to recent nerve construction research

Abstract

We show that the category of principal ordered face structures is equivalent to the category of multitopes. We show that the category of principal ordered face structures is equivalent to the category of multitopes. On the way we introduce the notion of a graded tensor theory to state the abstract properties of the category of ordered face structures and show how it fits into the recent work of T. Leinster and M. Weber concerning the nerve construction.