Fixed-color equivariant simplicial operads admit model structures whose weak equivalences are detected by graph subgroups or by any chosen (G,Sigma)-family of subgroups.
A Model Structure for Enriched Coloured Operads
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abstract
We prove that, under certain conditions, the model structure on a monoidal model category $\mathcal{V}$ can be transferred to a model structure on the category of $\mathcal{V}$-enriched coloured (symmetric) operads. As a particular case we recover the known model structure on simplicial operads.
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2019 1verdicts
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Homotopy theory of equivariant operads with fixed colors
Fixed-color equivariant simplicial operads admit model structures whose weak equivalences are detected by graph subgroups or by any chosen (G,Sigma)-family of subgroups.