Algebraic & Geometric Topology

Relative left properness of colored operads

Philip Hackney, Marcy Robertson, and Donald Yau

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The category of –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 –colored symmetric operads is not left proper.

Article information

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

Received: 1 December 2014
Revised: 9 December 2015
Accepted: 1 February 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D50: Operads [See also 55P48] 55U35: Abstract and axiomatic homotopy theory
Secondary: 18G55: Homotopical algebra 55P48: Loop space machines, operads [See also 18D50] 18D20: Enriched categories (over closed or monoidal categories)

operads model categories left proper


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.

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