Broad posets, trees, and the dendroidal category

TL;DR

This paper introduces an extension of order theory called broad posets, which provides a new formalism for studying dendroidal sets, similar to how order theory underpins the study of simplicial sets.

Contribution

It develops broad posets as a novel extension of order theory to facilitate the analysis of dendroidal sets.

Findings

Establishes a formal framework for broad posets.

Draws parallels between order theory and dendroidal sets.

Provides foundational tools for future research in the area.

Abstract

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.