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

Inthispaper, (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 MCS 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. 

Keywords:

Domain finiteness , M)-fuzzy (resp. stratified , weakly induced , induced) convex space , (L , M)-fuzzy restricted hull space , Galois correspondence , Coreflective