Abstract
If the standard concepts of partial-order relation and subset are fuzzied, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy join- semilattices, showing the analogy to the ordinary category Sup of join-semilattices.
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