Partially traced categories
Category Theory
2012-07-31 v2
Abstract
This paper deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully embedded in a totally traced category. Also conversely, every symmetric monoidal subcategory of a totally traced category is partially traced, so this characterizes the partially traced categories completely. The main technique we use is based on Freyd's paracategories, along with a partial version of Joyal, Street, and Verity's Int-construction.
Cite
@article{arxiv.1107.3608,
title = {Partially traced categories},
author = {Octavio Malherbe and Philip J. Scott and Peter Selinger},
journal= {arXiv preprint arXiv:1107.3608},
year = {2012}
}