A Categorical Isomorphism Between Injective Stratified Fuzzy $T_{\bm 0}$ Spaces and Fuzzy Continuous Lattices

For a frame
$L$
as the truth value table, we apply fuzzy domain theory for the study of injective objects in the category of stratified
$L$
-
$T_0$
spaces. We show that every fuzzy continuous lattice equipped with the fuzzy Scott topology is an injective stratified
$L$
-
$T_0$
space, and conversely, the specialization
$L$
-ordered set of an injective stratified
$L$
-
$T_0$
space is a fuzzy continuous lattice. These two transformations form a categorical isomorphism between injective stratified
$L$
-
$T_0$
spaces and fuzzy continuous lattices.