English

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Withdrawn.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

R2 v1 2026-06-22T14:53:54.850Z