#
The genuine operadic nerve

##
Peter Bonventre

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.

Keywords:
infinity operads, equivariant operads,symmetric monoidal categories

2010 MSC:
55P91,55P48,19D23,18D30

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 26, pp 736--780.

Published 2019-09-11.

http://www.tac.mta.ca/tac/volumes/34/26/34-26.pdf

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