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PreprintCC BY 4.0arXiv

Symmetric 2-rigs: coexponentiability and cartesian closure

  • Mathieu Anel
  • Marcelo Fiore
  • Nicola Gambino
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Abstract

We study coexponentiability in the context of the cocartesian 2-category RIG of symmetric 2-rigs, symmetric strong monoidal cocontinuous functors, and symmetric monoidal natural transformations. Our results characterize the coexponentiable symmetric 2-rigs as those that are deformation retracts of presheaf categories over small categories. As an application, we give an account of the cartesian closure of two full sub-2-categories of the dual of RIG arising from the theory of combinatorial species and the theory of symmetric operads.

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Cite

BibTeXRIS
BibTeX
@misc{anel2026symmetric,
  title = {{Symmetric 2-rigs: coexponentiability and cartesian closure}},
  author = {Mathieu Anel and Marcelo Fiore and Nicola Gambino},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.12683},
  eprint = {2607.12683},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12683},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Symmetric 2-rigs: coexponentiability and cartesian closure
AU  - Mathieu Anel
AU  - Marcelo Fiore
AU  - Nicola Gambino
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.12683
UR  - https://arxiv.org/abs/2607.12683
AB  - We study coexponentiability in the context of the cocartesian 2-category RIG of symmetric 2-rigs, symmetric strong monoidal cocontinuous functors, and symmetric monoidal natural transformations. Our results characterize the coexponentiable symmetric 2-rigs as those that are deformation retracts of presheaf categories over small categories. As an application, we give an account of the cartesian closure of two full sub-2-categories of the dual of RIG arising from the theory of combinatorial species and the theory of symmetric operads.
ER  -