On the combinatorics of faces of trees and anodyne extensions 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 pushoutproduct property for the stable model structure on dendroidal sets.2000 Mathematics Subject Classification. Primary: 55U05. Secondary: 55P48, 18G30.