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 $L$-{bf FCS} of $L$-fuzzy closure system spaces.