Symmetric 2-rigs: coexponentiability and cartesian closure

Mathieu Anel; Marcelo Fiore; Nicola Gambino

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arXiv · 2607.12683

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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Mathieu Anel, Marcelo Fiore, Nicola Gambino. 2026-07-14. Symmetric 2-rigs: coexponentiability and cartesian closure. https://arxiv.org/abs/2607.12683

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