Abstract
Many valued topologies on L-sets, providing a common framework for fuzzy topologies on fuzzy sets and the fixed-basis lattice-valued topologies on ordinary sets, are the main subject of the present study. In this paper, we have introduced many valued topological L-set-spaces, referring to L-sets equipped with many valued topologies, in an axiomatic way and focused on the vindication of their axiomatization in a categorical framework. In order to attain this objective, we apply the theory of Höhle of topological space objects formulated in terms of a partially ordered monad on an abstract category, and show that the category of many valued topological L-set-spaces is isomorphic to the category of topological space objects with respect to a partially ordered monad on a category of L-sets.
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