Bi-representable bi-multicategories

Bojana Femić

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arXiv · 2610.08454

Bi-representable bi-multicategories

Bojana Femić

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Abstract

We prove a two-dimensional version of Hermida's equivalence result on representable multicategories and classify its stricter versions. The obtained three-dimensional equivalence of the respective totality categories is of categories enriched over the multicategory $\mathsf{Bicat}$ of Verity. There is a basic enriched equivalence with respect to inherently lax monoidal pseudofunctors, and a one with respect to pseudo-monoidal pseudofunctors, related to the latter via the forgetful enriched functors. We extend Slattery's result on a bi-multicategory structure of the Kleisli bicategory of a 2-multicategory encompassing bi-representability.

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Bojana Femić. 2026-10-06. Bi-representable bi-multicategories. https://arxiv.org/abs/2610.08454

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