A Note on Categories about Rough Sets

Using the concepts of category and functor, we provide some insights and prove an intrinsic property of the category bf AprS of approximation spaces and relation-preserving functions, the category bf RCls of rough closure spaces and continuous functions, and the category bf RInt of rough interior spaces and continuous functions. Furthermore, we define the category bf IS of information systems and O-A-D homomorphisms, and establish the relationship between the category bf IS and the category bf AprS by considering a subcategory bf NeIS of bf IS whose objects are information systems and whose arrows are non-expensive O-A-D homomorphisms with surjective attribute mappings.