Categories of lattice-valued closure (interior) operators and Alexandro L-fuzzy topologies

Galois connection in category theory play an important role in establish the relationships between different spatial structures. In this paper, we prove that there exist many interesting Galois connections between the category of Alexandroff L-fuzzy topological spaces, the category of reflexive L-fuzzy approximation spaces and the category of Alexandroff L-fuzzy interior (closure) spaces. This indicates that there is a close connection between the three structures.