Compactification of *-autonomous categories
Logic in Computer Science
2016-07-21 v2 Category Theory
Logic
Abstract
We study the question when a *-autonomous (Mix-)category has a representation as a -autonomous category of a compact one. We prove that necessary and sufficient condition is that weak distributivity maps are monic (or, equivalently epic). For a Mix-category, this condition is, in turn, equivalent to the requirement that Mix-maps be monic (or epic). We call categories satisfying this property torsion-free. An important side result is that torsion-free categories have canonical partial traces.
Keywords
Cite
@article{arxiv.1607.03877,
title = {Compactification of *-autonomous categories},
author = {Sergey Slavnov},
journal= {arXiv preprint arXiv:1607.03877},
year = {2016}
}
Comments
Withdrawn. The author found a stupid diverging loophole in a proof, and the announced result is false anyway