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This paper develops a new locale action, revealing a functor mapping topological directed weak L-modules to directed complete L-slices.
A new notion of action of a locale L on P is developed in the context of point free topology, given a locale L and a directed complete join semilattice P with bottom element 0P. This work establishes the existence of a contravariant functor from the category TopDWMod of topological directed weak L-modules and continuous weak L-module homomorphisms to the category DL-slice of directed complete L-slices and directed complete L-slice homomorphisms.
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Sabna et al. (2025) studied this question.
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