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摘要
En 中文
For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By constructing continuous relations that naturally generalize continuous maps, it is shown (in the generality of the Q-version) that the category of closure spaces and closed continuous relations is equivalent to the category of complete lattices and sup-preserving maps. (C) 2016 Elsevier B.V. All rights reserved.
Keyword:
Quantaloid
Q-closure space
Continuous Q-functor
Continuous Q-distributor
Continuous Q-relation
Complete Q-category
Fuzzy closure space
Fuzzy powerset
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