Categories isomorphic to the category of L-fuzzy closure system spaces

In this paper, new definitions of L-fuzzy closure operator, L-fuzzy interior operator, L-fuzzy remote neighborhood system, L-fuzzy neighborhood system and L-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of L-fuzzy closure spaces, the category of L-fuzzy interior spaces, the category of L-fuzzy remote neighborhood spaces, the category of L-fuzzy quasi-coincident neighborhood spaces, the category of L-fuzzy neighborhood spaces are all isomorphic to the category L-FCS of L-fuzzy closure system spaces.