  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.
