Minimal fibrations of dendroidal sets

Moerdijk, Ieke; Nuiten, Joost

doi:10.2140/agt.2016.16.3581

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Minimal fibrations of dendroidal sets

Ieke Moerdijk and Joost Nuiten

Algebraic & Geometric Topology 16 (2016) 3581–3614

DOI: 10.2140/agt.2016.16.3581

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 $Γ$ –spaces).

Keywords

minimal fibrations, dendroidal sets, Gamma-spaces, Reedy categories

Mathematical Subject Classification 2010

Primary: 55R65, 55U35, 55P48

Secondary: 18D50

References

Publication

Received: 3 December 2015

Revised: 5 April 2016

Accepted: 29 April 2016

Published: 15 December 2016

Authors

Ieke Moerdijk
Mathematical Institute Utrecht University PO Box 80010 3508 TA Utrecht Netherlands

Joost Nuiten
Mathematical Institute Utrecht University P.O. Box 80010 3508 TA Utrecht Netherlands

Volume 16, issue 6 (2016)