Re: "Databases are Categories"

["Mattias Wikström" <mattias.wikstrom@gmail.com>]

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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