Duality between data and process: an enriched categorical point of view

Abstract

Enriched categories have been shown to be an important tool in understanding the nature of distributed computation ([KL10]). Of particular interest is the characterization of processes by means of experiments and observers ([KL91]). Database theory is an active field of research with many theoretical and technical problems still to be solved. As described in [JR07], category theory has been shown to be an effective way of dealing with various aspects of databases. This talk discusses how an enriched categorical framework can be applied to databases. To this end, we will describe three approaches enriched over the same bicategory: 1) considers a fixed database state with views as experiments in the sense of [KL91], 2) considers variable database states and uses a view ([JR07]) as the enrichment, 3) considers the sequences of SQL operations that led to a particular database state enriched as in [KL99]. Approaches 2) and 3) exhibit the process-data duality, and we will show that they are components of a single mathematical object: they take part in a two-sided enrichment in the sense of [KLSS02]. References: [JR07] M. Johnson, R. Rosebrugh. Fibrations and universal view updatability. Theor.Comput.Sci., 388(1-3):109-129, 2007; [KL91] S. Kasangian, A. Labella. On continuous time agents. In S.D. Brookes, M.G. Main, A. Melton, M.W. Mislove, D.A. Schmidt, eds., MFPS, volume 598 of Lecture Notes in Computer Science, pages 403-425. Springer, 1991; [KL99] S. Kasangian, A. Labella. Observational trees as models for concurrency. Mathematical Structures in Comp.Sci., 9(6):687-718, 1999; [KL10] S. Kasangian, A. Labella. Conduch property and Tree-based categories. Journal of Pure and Applied Algebra, 214(3):221-235, 2010; [KLSS02] M. Kelly, A. Labella, V. Schmitt, R. Street. Categories enriched on two sides. Journal of Pure and Applied Algebra, 168(1):53–98, 2002

Date
Location
Genova, Italy