Dendroidal sets as models for connective spectra

TL;DR

This paper establishes a new combinatorial model using dendroidal sets for homotopy coherent operads and proves its equivalence to the homotopy theory of connective spectra.

Contribution

It introduces fully Kan dendroidal sets and constructs a model structure where these are the fibrant objects, linking dendroidal sets to connective spectra.

Findings

Model structure on dendroidal sets with fully Kan objects

Equivalence between dendroidal set homotopy theory and connective spectra

Fibrant objects characterized by fully Kan dendroidal sets

Abstract

Dendroidal sets have been introduced as a combinatorial model for homotopy coherent operads. We introduce the notion of fully Kan dendroidal sets and show that there is a model structure on the category of dendroidal sets with fibrant objects given by fully Kan dendroidal sets. Moreover we show that the resulting homotopy theory is equivalent to the homotopy theory of connective spectra.