About five months ago I gave a talk here at Galois called “Databases are categories.” The basic idea was that a database schema can be represented as a category C and its states can be represented as functors C–>Set. In this talk I’ll refine that notion a bit, explaining that schemas are better represented as sketches. I’ll also show how, within this model one can: deal with incomplete data; incorporate typing and calculated fields; and perform queries, define views, and migrate data between disparate schemas. That is, I’ll try to show that the categorical approach handles everything one might hope it would. Finally, I’ll discuss a linguistic version of categories, called “ologs,” and show how they may help to democratize information storage.
I received my PhD in mathematics from UC Berkeley in 2007; my thesis was in Algebraic Topology. For the next three years I was a post doc in the math department at the University of Oregon. During this time my focus moved toward using category theory to understand information and communication. This past summer (2010) I began a post doc in the math department at MIT. My main interest at the moment is in using category theory to bridge the gap between disparate academic fields, and to generally enhance our ability to record, process, and communicate information.
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