## Algebraic & Geometric Topology

### Relative left properness of colored operads

#### Abstract

The category of $ℭ$–colored symmetric operads admits a cofibrantly generated model category structure. In this paper, we show that this model structure satisfies a relative left properness condition, ie that the class of weak equivalences between $Σ$–cofibrant operads is closed under cobase change along cofibrations. We also provide an example of Dwyer which shows that the model structure on $ℭ$–colored symmetric operads is not left proper.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2691-2714.

Dates
Revised: 9 December 2015
Accepted: 1 February 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841225

Digital Object Identifier
doi:10.2140/agt.2016.16.2691

Mathematical Reviews number (MathSciNet)
MR3572345

Zentralblatt MATH identifier
1350.18016

#### Citation

Hackney, Philip; Robertson, Marcy; Yau, Donald. Relative left properness of colored operads. Algebr. Geom. Topol. 16 (2016), no. 5, 2691--2714. doi:10.2140/agt.2016.16.2691. https://projecteuclid.org/euclid.agt/1510841225

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