Dear colleagues, we just put a new paper on the ArXiv about partially traced categories. They are almost the same thing as traced monoidal categories (a la Joyal, Street, and Verity 1996), except that the trace is a partially defined operation, subject to some axioms. The main result is a representation theorem: every partially traced category can be faithfully embedded in a totally traced category (and conversely, every symmetric monoidal subcategory of a totally traced category is partially traced; thus this representation theorem completely characterizes partially traced categories). Interestingly, there are some naturally occuring examples of partially traced categories (such as on the category of vector spaces with direct sum as the monoidal structure) that do not appear to be embedded in any *naturally occuring* totally traced category (i.e., other than the one constructed by the completeness theorem). The details of the paper appear below. Best wishes, -- Octavio, Phil, and Peter ---------------------------------------------------------------------- Partially traced categories Octavio Malherbe, Philip J. Scott, Peter Selinger http://arxiv.org/abs/1107.3608 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. ---------------------------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]