Symmetric 2-rigs: coexponentiability and cartesian closure
arXiv:2607.12683
The paper investigates which symmetric 2‑rig structures can be coexponentiated, showing they are exactly deformation retracts of presheaf categories, and uses this to describe cartesian closed sub‑2‑categories related to combinatorial species and symmetric operads.
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.
14 pages. Comments welcome