language-icon Old Web
English
Sign In

The genuine operadic nerve

2019 
We construct a generalization of the operadic nerve, providing a translation between the equivariant simplicially enriched operadic world to the parametrized $\infty$-categorical perspective. This naturally factors through genuine equivariant operads, a model for "equivariant operads with norms up to homotopy". We introduce the notion of an op-fibration of genuine equivariant operads, extending Grothendieck op-fibrations, and characterize fibrant operads as the image of genuine equivariant symmetric monoidal categories. Moreover, we show that under the operadic nerve, this image is sent to $G$-symmetric monoidal $G$-$\infty$-categories. Finally, we produce a functor comparing the notion of algebra over an operad in each of these two contexts.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    34
    References
    4
    Citations
    NaN
    KQI
    []