Further results on $L$-ordered fuzzifying convergence spaces

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying convergence spaces can be embedded in the category of stratified $L$-ordered convergence spaces as a coreflective subcategory.