Minimal fibrations of dendroidal sets

@article{Moerdijk2015MinimalFO,
  title={Minimal fibrations of dendroidal sets},
  author={Ieke Moerdijk and Joost Nuiten},
  journal={arXiv: Algebraic Topology},
  year={2015}
}
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… 
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References

SHOWING 1-10 OF 34 REFERENCES
Dendroidal sets as models for connective spectra
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…
Algebras over infinity-operads
We develop a notion of an algebra over an infinity-operad with values in infinity-categories which is completely intrinsic to the formalism of dendroidal sets. Its definition involves the notion of a…
The geometric realization of a Kan fibration is a Serre fibration
The object of this note is to prove the statement in the title which is asserted without proof in [1, Lemma 2.1]. We follow the terminology of [2, II, 3] except that a map of simplicial sets which is…
Note on the tensor product of dendroidal sets
In our paper "Dendroidal sets as models for homotopy operads" (J. Topol. 4 (2011), no. 2, 257-299, and arXiv:0902.1954), we made the wrong claim about the behaviour of the tensor product with respect…
Dendroidal sets and simplicial operads
We establish a Quillen equivalence relating the homotopy theory of Segal operads and the homotopy theory of simplicial operads, from which we deduce that the homotopy coherent nerve functor is a…
On inner Kan complexes in the category of dendroidal sets
Univalent universes for elegant models of homotopy types
We construct a univalent universe in the sense of Voevodsky in some suitable model categories for homotopy types (obtained from Grothendieck's theory of test categories). In practice, this means for…
Fibrations and homotopy colimits of simplicial sheaves
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition,…
Erratum to “Left-determined model categories and universal homotopy theories”
We say that a model category is left-determined if the weak equivalences are generated (in a sense specified below) by the cofibrations. While the model category of simplicial sets is not…
Simplicial Methods for Operads and Algebraic Geometry
Lectures on Dendroidal Sets.- Operads.- Trees as operads.- Dendroidal sets.- Tensor product of dendroidal sets.- A Reedy model structure on dendroidal spaces.- Boardman-Vogt resolution and homotopy…
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