Operadic 2-rigs — Draconitic Research

Abstract

We show that the bicategory of operads and bimodules can be embedded into the bicategory of symmetric 2-rigs, a categorification of commutative rings. In order to do this, we introduce the notion of an operadic 2-rig and show that the full sub-bicategory of symmetric 2-rigs spanned by operadic 2-rigs has the universal property of being a completion under Eilenberg-Moore-Kleisli objects.

Binomial coefficients and the operadic butterfly
Vladimir Dotsenko, Medet Jumadildayev
arXiv27 Sep 2026PreprintarXiv licenceFull textAlgebra & number theory Combinatorics & discrete mathematicsarXiv
Symmetric 2-rigs: coexponentiability and cartesian closure
Mathieu Anel, Marcelo Fiore, Nicola Gambino
arXiv1 Oct 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv

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BibTeX

@misc{anel2026operadic,
  title = {{Operadic 2-rigs}},
  author = {M. Anel and M. Fiore and N. Gambino},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.12705},
  eprint = {2607.12705},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12705},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Operadic 2-rigs
AU  - M. Anel
AU  - M. Fiore
AU  - N. Gambino
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.12705
UR  - https://arxiv.org/abs/2607.12705
AB  - We show that the bicategory of operads and bimodules can be embedded into the bicategory of symmetric 2-rigs, a categorification of commutative rings. In order to do this, we introduce the notion of an operadic 2-rig and show that the full sub-bicategory of symmetric 2-rigs spanned by operadic 2-rigs has the universal property of being a completion under Eilenberg-Moore-Kleisli objects.
ER  -

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