A topological category of pretopological \(L\)-fuzzy \(Q\)-convergence spaces is constructed, which contains the category of topological \(L\)-fuzzy \(Q\)-convergence spaces as a bireflective full subcategory. It is proved that the category of topological \(L\)-fuzzy \(Q\)-convergence spaces is isomorphic to the category of topological \(L\)-fuzzy quasi-coincident neighborhood spaces, which is isomorphic to the category of \(L\)-fuzzy topological spaces. It is shown that the studied pretopological \(L\)-fuzzy \(Q\)-convergence spaces can be characterized as a kind of \(L\)-fuzzy quasi-coincident neighborhood spaces.