English

The genuine operadic nerve

Algebraic Topology 2021-06-04 v2

Abstract

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 GG-symmetric monoidal GG-\infty-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

R2 v1 2026-06-23T08:26:57.296Z