I think it makes sense to regard database schemas as theories and databases as models of such theories. Given a theory T that models some database schema S, a term in the language of T may be thought of as a "database query" (to obtain the result of the query, simplify the term), while a statement that two terms in the language of T are equal may be thought of as a "database constraint" that one may want to add to S. (In practise, though, one may want to formulate ones queries and contraints not in the language of T but in languages somehow obtained from that language.) What sort of theory should a database schema be? This surely depends on what exactly one is trying to model: A schema in Company A's DBMS (database management system) is rarely the same thing as a schema in Company B's DBMS, and in any case one probably wants to work with some idealised mathematical model. David Spivak seems to offer two different answers. On the one hand, a database schema may be the same thing as a category. On the other hand, a database schema may be a labeled simplicial set. Both answers may be found at http://www.uoregon.edu/~dspivak/cs/ . Mattias Wikstrom ----------------------------------------
Date: Mon, 9 Aug 2010 11:12:34 -0500 Subject: categories: "Databases are Categories" (again) From: vigalchin@gmail.com To: categories@mta.ca
Hello,
I stumbled across this tech talk: http://www.galois.com/blog/2010/05/27/tech-talk-categories-are-databases/ I was wondering what others in this mail list think about Spivak's thesis. I apologize if already posted.
Regards,
Vasili
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