Data Base Mappings and Monads: (Co)Induction
This paper presented the semantics of database mappings in the relational DB category based on the power-view monad T and monadic algebras. The objects in this category are the database-instances (A database-instance is a set of n-ary relations, i.e., a set of relational tables as in standard RDBs). The morphisms in DB category are used in order to express the semantics of view based Global and Local As View (GLAV) mappings between relational databases, for example those used in Data Integration Systems. Such morphisms in this DB category are not functions but have the complex tree structures based on a set of complex query computations between two database-instances.