A Duality of Quantale-Enriched Categories
Dirk Hofmann, Pawel Waszkiewicz
TL;DR
This paper establishes a duality for quantale-enriched categories that generalizes Lawson duality for continuous dcpos, highlighting a self-dual structure under specific conditions involving modules and morphisms.
Contribution
It extends Lawson duality to a broader class of quantale-enriched categories using a new duality framework involving modules and weighted limits.
Findings
Category of J-cocomplete and J-continuous quantale-enriched categories is self-dual.
Duality applies to categories with modules that commute with weighted limits.
Generalizes Lawson duality for continuous dcpos.
Abstract
We describe a duality for quantale-enriched categories that extends the Lawson duality for continuous dcpos: for any saturated class J of modules that commute with certain weighted limits, and under an appropriate choice of morphisms, the category of J-cocomplete and J-continuous quantale-enriched categories is self-dual.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras