Colloquium Details
Databases from a category-theoretic perspective
| Author: | David Spivak University of Oregon |
|---|---|
| Date: | February 07, 2008 |
| Time: | 15:30 |
| Location: | 220 Deschutes |
| Host: | Dejing Dou |
Abstract
Category theory arose in the 1940s as a way provide a single framework in which many different mathematical disciplines can be represented. A category roughly consists of objects and relationships between them, and a functor is a way of relating one category to another. This approach is both flexible and powerful, and is ubiquitous in mathematical research today. One might say that a category theorist studies the structure of mathematics.
In this talk we will lay out the basics of category theory and then quickly dive into the theory of relational databases. We can formulate relational databases in a categorical manner, and show how joins, selection, and projection queries are natural from this perspective. One nice result of our approach is that joins or projections of databases are naturally databases: one does not need to delve into the dubious theory of multi-sets. Another nice result is that the definitions of the various query operations are simultaneously prescriptions for carrying them out. Finally, our approach can be useful in database integration problems.
Biography
David Spivak received his BS from the University of Maryland, and his PhD from the University of California, Berkeley; both degrees were in Mathematics. Currently, he is a post doc at the University of Oregon in the math department. His main area of research is category theory and its applications, especially to algebraic topology. Recently he has begun to look into applications of category theory to other academic disciplines, especially to computer science.