Category and subcategories of (L, M)-fuzzy convex spaces

In this paper, (L, M)-fuzzy domain finiteness and (L, M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L, M)-CS of (L, M)-fuzzy convex spaces are obtained. Then, (L, M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L, M)-SCS of (L, M)-fuzzy stratified convex spaces and the category (L, M)-WICS of (L, M)-fuzzy weakly induced convex spaces, are coreflective subcategories of (L, M)-CS. It is also proved that three isomorphic categories, namely, the category M-CS of M-fuzzifying convex spaces, the category (L, M)-CGCS of (L, M)-fuzzy convex spaces induced by M-fuzzifying convex spaces and the category (L, M)-ICS of (L, M)-fuzzy induced convex spaces, are coreflective subcategories of both (L, M)-SCS and (L, M)-WICS.