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.