Subcategories of the category of stratified (L, M)-semiuniform convergence tower spaces

In this paper, we propose the concepts of stratified (L, M)-semiuniform convergence spaces and stratified (L, M)-semiuniform limit tower spaces. It is shown that (1) the category S(L, M)-SUC of stratified (L, M)-semiuniform convergence spaces can be embedded in the category S(L, M)-SUCT of stratified (L, M)-semiuniform convergence tower spaces as a bireflective subcategory; (2) the full subcategory of S(L, M)-SUCT, consisting of stratified (L, M)-semiuniform limit tower spaces is strongly Cartesian closed; (3) the category S(L, M)-FT of stratified (L, M)-filter tower spaces can be embedded in the category S(L, M)-SUCT as a simultaneously bireflective and bicoreflective subcategory.