Compactification of *-autonomous categories

Sergey Slavnov

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arXiv · 1607.03877

Compactification of *-autonomous categories

Sergey Slavnov

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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.

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Sergey Slavnov. 2016-07-13. Compactification of *-autonomous categories. https://arxiv.org/abs/1607.03877

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