Abstract
This paper introduces a special Galois connection combined with the wedge-below relation. Furthermore, by using this tool, it is shown that the category of M-fuzzifying betweenness spaces and the category of M-fuzzifying convex spaces are isomorphic and the category of arity-2 M-fuzzifying convex spaces can be embedded in the category of M-fuzzifying interval spaces as a reflective subcategory.
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