The genuine operadic nerve
Abstract
We construct a generalization of the operadic nerve, providing a translation between the equivariant simplicially enriched operadic world to the parametrized -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 -symmetric monoidal --categories. Finally, we produce a functor comparing the notion of algebra over an operad in each of these two contexts.
Keywords
Cite
@article{arxiv.1904.01465,
title = {The genuine operadic nerve},
author = {Peter Bonventre},
journal= {arXiv preprint arXiv:1904.01465},
year = {2021}
}
Comments
Comments welcome! v2: 39 pages. Strengthened Thm II to include simplicial enrichments, added examples and comparisons of algebras, general revisions. v1: 38 pages