2011/02/22 by Zoran Majkic, Zoran Majkić, Majkic, Zoran
Computer Science · Mathematics · #Advanced Database Systems and Queries #Category Theory (math.CT) #Databases (cs.DB) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Parallel Computing and Optimization Techniques #cs.DB #cs.LO #math.CT
paper · pdf · doi:10.48550/arxiv.1102.4769
31 pages
arxiv created 2011/02/22 · openalex publication_date 2011/02/22 · arxiv updated 2011/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we 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. Thus DB category, as a base category for the semantics of databases and mappings between them, is different from the Set category used dominantly for such issues, and needs the full investigation of its properties. In this paper we presented another contributions for an intensive exploration of properties and semantics of this category, based on the power-view monad T and the Kleisli category for databases. Here we stressed some Universal algebra considerations based on monads and relationships between this DB category and the standard Set category. Finally, we investigated the general algebraic and induction properties for databases in this category, and we defined the initial monadic algebras for database instances.