Relative left properness of colored operads

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 $\Sigma$-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.

To appear in Algebraic & Geometric Topology

References in corpus (1)

• Dendroidal sets and simplicial operads

Cited by in corpus (5)

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• The homotopy theory of simplicial props
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