PreprintCC BY-NC-ND 4.0arXiv
Bi-representable bi-multicategories
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 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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BibTeX
@misc{femic2026birepresentable,
title = {{Bi-representable bi-multicategories}},
author = {Bojana Femić},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08454},
eprint = {2610.08454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08454},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bi-representable bi-multicategories
AU - Bojana Femić
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08454
UR - https://arxiv.org/abs/2610.08454
AB - 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 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.
ER -