Aggregation functions are precisely the lax morphisms of quantales, supplying a unified framework that deduces prior results on metric and fuzzy metric aggregation.
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2026 2verdicts
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Quasi-pseudometric modular spaces with nonexpansive maps form a category isomorphic to one enriched over a quantale of isotone functions, with matching induced topologies, and quasi-pseudometrizable spaces coincide exactly with those from quasi-pseudometric modulars.
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Aggregation functions as lax morphisms of quantales
Aggregation functions are precisely the lax morphisms of quantales, supplying a unified framework that deduces prior results on metric and fuzzy metric aggregation.
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Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories
Quasi-pseudometric modular spaces with nonexpansive maps form a category isomorphic to one enriched over a quantale of isotone functions, with matching induced topologies, and quasi-pseudometrizable spaces coincide exactly with those from quasi-pseudometric modulars.