Relative left properness of colored operads

Hackney, Philip¹ ; Robertson, Marcy² ; Yau, Donald³

¹Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
²School of Mathematics and Statistics, University of Melbourne, Melbourne ACT 3010, Australia
³Department of Mathematics, The Ohio State University at Newark, Newark, OH 43055, United States

Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2691-2714

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.2691

Classification : 18D50, 55U35, 18G55, 55P48, 18D20
Keywords: operads, model categories, left proper

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