Dendroidal spaces, $\Gamma$-spaces and the special Barratt-Priddy-Quillen theorem

TL;DR

This paper explores the connections between dendroidal spaces, $ ext{ extGamma}$-spaces, and the Barratt-Priddy-Quillen theorem, advancing the understanding of homotopy theories related to operads and special $ extGamma$-spaces.

Contribution

It establishes direct relations between the covariant model structure on dendroidal spaces and the homotopy theory of algebras over simplicial operads, including a refined Barratt-Priddy-Quillen theorem.

Findings

Established a covariant model structure on dendroidal spaces.

Linked dendroidal spaces to homotopy theory of $ extGamma$-spaces.

Sharpened the classical Barratt-Priddy-Quillen theorem.

Abstract

We study the covariant model structure on dendroidal spaces and establish direct relations to the homotopy theory of algebras over a simplicial operad as well as to the homotopy theory of special $\Gamma$-spaces. As an important tool in the latter comparison, we present a sharpening of the classical Barratt-Priddy-Quillen theorem.