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Considering  L  as a complete residuated lattice, some further investigations on  L -filter spaces are made. Firstly, it is shown that the category  L - Fil  of  L -filter spaces is monoidal closed. Secondly, it is proved that the categories of  L -Cauchy spaces and  L -semi-Cauchy spaces are both bireflective subcategories of  L - Fil . Finally, the concept of filter-determined  L -semiuniform convergence spaces is proposed and the resulting category is shown to be isomorphic to  L - Fil , which can be embedded in the category of  L -semiuniform convergence spaces as a bicoreflective subcategory. Moreover, it is proved that  L - Fil  can be embedded in the category of  L -semiuniform convergence spaces as a bireflective subcategory whenever  L  is a completely distributive lattice.

The category of residuated lattice valued filter spaces