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-T0 spaces. We show that every fuzzy continuous lattice equipped with the fuzzy Scott topology is an injective stratified L-T0 space, and conversely, the specialization L-ordered set of an injective stratified L-T0 space is a fuzzy continuous lattice. These two transformations form a categorical isomorphism between injective stratified L-T0 spaces and fuzzy continuous lattices.

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