On the combinatorics of faces of trees and anodyne extensions of dendroidal sets

TL;DR

This paper explores the combinatorial structure of tree faces in dendroidal sets and establishes the pushout-product property for their stable model structure, advancing the understanding of dendroidal homotopy theory.

Contribution

It provides a systematic treatment of dendroidal anodyne extensions and proves the pushout-product property, a key result in dendroidal set theory.

Findings

Developed a systematic approach to dendroidal anodyne extensions

Proved the pushout-product property for the stable model structure

Enhanced the theoretical framework of dendroidal sets

Abstract

We discuss the combinatorics of faces of trees in the context of dendroidal sets and develop a systematic treatment of dendroidal anodyne extensions. As the main example and our motivation, we prove the pushout-product property for the stable model structure on dendroidal sets.