Minimal fibrations of dendroidal sets

Abstract

We prove the existence of minimal models for fibrations between dendroidal sets in the model structure for $\infty$–operads, as well as in the covariant model structure for algebras and in the stable one for connective spectra. We also explain how our arguments can be used to extend the results of Cisinski (2014) and give the existence of minimal fibrations in model categories of presheaves over generalized Reedy categories of a rather common type. Besides some applications to the theory of algebras over $\infty$–operads, we also prove a gluing result for parametrized connective spectra (or $\Gamma$–spaces).