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• W2342488770 abstract "Thispaperdealswithaparticularquestion—Whendopowersetsinlattice-valuedmathematicsformalgebraictheories(ormonads) incloneform?Ourapproachinthisandrelatedpapersistoconsider “powersetsoverobjects”inthegroundcategoriesSetandSet×C 9 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 Set × C, necessary and sufficient 11 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. 13" @default.
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• W2342488770 date "2009-01-01" @default.
• W2342488770 modified "2023-09-27" @default.
• W2342488770 title "Relationship of algebraic theories to powersets over objects in Set" @default.
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