PreprintarXiv licencearXiv
The 2-monoidal structure of symmetric sequences
Abstract
We prove a conjecture proposed by Dwyer and Hess (2014), namely that the category of symmetric sequences, when equipped with the composition and matrix monoidal structures, forms a 2-monoidal category in the sense of Aguiar and Mahajan (2010). Our approach leverages a detailed analysis of the interplay between these two monoidal structures, offering new insights into their behavior. As a consequence, we are able to show that every operad admits a Day-operad structure.
Related
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- Actions of central Morita monoidal groupoids, and seven term exact sequences of all types
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BibTeX
@misc{dan20262monoidal,
title = {{The 2-monoidal structure of symmetric sequences}},
author = {Patrick Dan and Claudio Pfammatter},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29075},
eprint = {2608.29075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29075},
}
RIS
TY - UNPB
TI - The 2-monoidal structure of symmetric sequences
AU - Patrick Dan
AU - Claudio Pfammatter
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29075
UR - https://arxiv.org/abs/2608.29075
AB - We prove a conjecture proposed by Dwyer and Hess (2014), namely that the category of symmetric sequences, when equipped with the composition and matrix monoidal structures, forms a 2-monoidal category in the sense of Aguiar and Mahajan (2010). Our approach leverages a detailed analysis of the interplay between these two monoidal structures, offering new insights into their behavior. As a consequence, we are able to show that every operad admits a Day-operad structure.
ER -