Characterizations of M-fuzzifying convex spaces via Galois connections

This is the authors' abstract. We don't add key points for this paper.

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.