PreprintCC BY 4.0arXiv
The symmetric skew monoidal structure of Gray-categories
Abstract
In previous work, we constructed a closed skew monoidal structure on the category of Gray-categories and Gray-functors whose internal hom Psd(A, B) captures pseudomaps and pseudo-transformations. In the present paper we give a symmetric description of the Gray-category Psd(A,B) and use this to prove that the skew monoidal structure is symmetric skew monoidal.
Related
BibTeX
@misc{bourke2026symmetric,
title = {{The symmetric skew monoidal structure of Gray-categories}},
author = {John Bourke and Gabriele Lobbia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31410},
eprint = {2610.31410},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31410},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The symmetric skew monoidal structure of Gray-categories
AU - John Bourke
AU - Gabriele Lobbia
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.31410
UR - https://arxiv.org/abs/2610.31410
AB - In previous work, we constructed a closed skew monoidal structure on the category of Gray-categories and Gray-functors whose internal hom Psd(A, B) captures pseudomaps and pseudo-transformations. In the present paper we give a symmetric description of the Gray-category Psd(A,B) and use this to prove that the skew monoidal structure is symmetric skew monoidal.
ER -