A comparison of lattice-theoretic approaches to fuzzy topology
Fuzzy Sets and Systems
Abstract and concrete categories
Abstract and concrete categories
Point-set lattice-theoretic topology
Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
A general theory of fuzzy topological spaces
Fuzzy Sets and Systems - Special issue on fuzzy topology
Some remarks on fuzzy powerset operators
Fuzzy Sets and Systems
A categorical accommodation of various notions of fuzzy topology
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Categories of lattice-valued sets as categories of arrows
Fuzzy Sets and Systems
Hypergraph functor and attachment
Fuzzy Sets and Systems
Generalized fuzzy topology versus non-commutative topology
Fuzzy Sets and Systems
A survey of fuzzifications of frames, the Papert--Papert--Isbell adjunction and sobriety
Fuzzy Sets and Systems
Categorical foundations of variety-based topology and topological systems
Fuzzy Sets and Systems
Categorically algebraic topology versus universal topology
Fuzzy Sets and Systems
On fuzzification of topological categories
Fuzzy Sets and Systems
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This paper deals with a particular question-When do powersets in lattice-valued mathematics form algebraic theories (or monads) in clone form? Our approach in this and related papers is to consider ''powersets over objects'' in the ground categories Set and SetxC from the standpoint of algebraic theories in clone form (C is a particular subcategory of the dual of the category of semi-quantales). For both fixed-basis powersets over objects of Set and variable-basis powersets over objects of SetxC, necessary and sufficient conditions are found under which the family of all such powersets over a ground object forms an algebraic theory in clone form of standard construction. In such results a distinguished role emerges for unital quantales.