# 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…

## 10 Citations

Profinite $\infty$-operads

- Mathematics
- 2021

We show that a profinite completion functor for (simplicial or topological) operads with good homotopical properties can be constructed as a left Quillen functor from an appropriate model category of…

Note on the tensor product of dendroidal sets

- Mathematics
- 2014

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…

Localizing infinity-categories with hypercovers

- Mathematics
- 2016

Given an $\infty$-category with a set of weak equivalences which is stable under pullback, we show that the mapping spaces of the corresponding localization can be described as group completions of…

LOCALIZING ∞-CATEGORIES WITH HYPERCOVERS

- Mathematics
- 2020

Given an ∞-category with a set of weak equivalences which is stable under pullback, we show that the mapping spaces of the corresponding localization can be described as group completions of…

Dendroidal spaces, Γ-spaces and the special Barratt--Priddy--Quillen theorem

- Mathematics
- 2018

Abstract We study the covariant model structure on dendroidal spaces, and establish direct relations to the homotopy theory of algebras over a simplicial operad as well as to the homotopy theory of…

Twisted arrow categories, operads and Segal conditions

- Mathematics
- 2021

We introduce twisted arrow categories of operads and of algebras over operads. Up to equivalence of categories, the simplex category ∆ , Segal’s category Γ , Connes cyclic category Λ , Moerdijk–Weiss…

On factorizations of graphical maps

- Mathematics
- 2017

We study the categories governing infinity (wheeled) properads. The graphical category, which was already known to be generalized Reedy, is in fact an Eilenberg-Zilber category. A minor alteration to…

Uniform Fibrations and the Frobenius Condition

- Mathematics
- 2015

We introduce and study the notion of a uniform fibration in categories with a functorial cylinder. In particular, we show that in a wide class of presheaf categories, including simplicial sets and…

## References

SHOWING 1-10 OF 34 REFERENCES

Dendroidal sets as models for connective spectra

- Mathematics
- 2012

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

- Mathematics
- 2011

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

- Mathematics
- 1968

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

- Mathematics
- 2014

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

- Mathematics
- 2013

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…

Univalent universes for elegant models of homotopy types

- Mathematics
- 2014

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

- Mathematics
- 1998

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”

- Mathematics
- 2008

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

- Mathematics
- 2010

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…