  U. H{\"o}hle and A. {\v{S}}ostak have developed in \cite{HS} the category of
complete quasi-monoidal lattices; S. E. Rodabaugh in \cite{RO} proposed its
opposite category and with a subcategory $\mathbf{C}$ of the latter, he define
grounds of the form $\mathbf{SET\times C}$. In this paper, for each ground
category of the form $\mathbf{SET\times C}$, we study categorical frameworks
for variable-basis fuzzy filters, particularly the category $\mathbf{C-FFIL}$
of variable-basis fuzzy filters, as a natural generalization of the category of
fixed-basis fuzzy filters which was introduced in \cite{LO}. In addition, we
get some relations between the category of variable-basis fuzzy filters and the
category of variable-basis fuzzy topological spaces.
