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arXiv · 1411.4668

Relative left properness of colored operads

Philip Hackney·Marcy Robertson·Donald Yau
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Abstract

The category of $\mathfrak{C}$-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, i.e., 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 $\mathfrak{C}$-colored symmetric operads is not left proper.

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Philip Hackney, Marcy Robertson, Donald Yau. 2016-10-03. Relative left properness of colored operads. https://doi.org/10.2140/agt.2016.16.2691

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