The free compact closure of a symmetric monoidal category
Abstract
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original category. The symmetric monoidal category embeds via a faithful monoidal functor into its completion, but in contrast to the non-symmetric case, this embedding is not full. Our construction factors through the Int construction, which yields another free construction: the free traced monoidal category on a symmetric monoidal category.
Keywords
Cite
@article{arxiv.2201.07527,
title = {The free compact closure of a symmetric monoidal category},
author = {Antonin Delpeuch},
journal= {arXiv preprint arXiv:2201.07527},
year = {2022}
}
Comments
This paper contains a serious mistake and the claimed results are invalid. This construction cannot work, because of an observation by Plotkin: ncatlab.org/nlab/show/traced+monoidal+category#adding_traces. Thanks go to Robin Kaarsgaard for pointing this out