Minimal fibrations of dendroidal sets

TL;DR

This paper establishes the existence of minimal fibrations across various model structures related to infinity-operads, algebras, and spectra, with applications to algebraic and homotopical contexts.

Contribution

It introduces the first proof of minimal fibrations for dendroidal sets in multiple model structures and extends these results to presheaves over generalized Reedy categories.

Findings

Existence of minimal models for fibrations in dendroidal sets.

Extension of minimal fibration results to presheaves over Reedy categories.

A gluing theorem for parametrized connective spectra.

Abstract

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