Re: Basic question?What 's the key if there 's no FD(Functional Dependencies)?

NENASHI, Tegiri wrote:
> vc wrote:
> > NENASHI, Tegiri wrote:
> > [...]
> > > There is better thing for database abstraction. Theory of categories is
> > > very good for abstraction. Its better than sets because you do not
> > > need to think of not important details. Category theory and relational
> > > theory is like algebra and multiplication table. Do you want to use
> > > algebra or still arithmetic ?
> >
> > That does not make any obvious sense. What specific advantages that
> > "the theory of categories" might have in comparison to the relational
> > model do you have in mind ?
>
> The advantage is a lot: evolution from functional datamodel DAPLEX to
> the functorial data mode: class is a category; arrows in the category
> are methods or depenedncies Arrows domain and codomain can be SET
> category but can be other category; functional dependencies can be
> composed because they are arrows; relationships are pullbacks;
> inheritance is a coproduct; primary key is the initial object in the
> category; et cetera. If XML inventors knew category theory then XML
> would be useful very much more. Zinovy Diskin said that category theory
> is only real algebra for graphs and nets.
>
>
> >Are you familiar with relational database
> > theory and implementations ?
>
> I studied Codd and Date and utilized Postgress and Oracle.
>
> >Besides, it's not "the theory of
> > categories" but "category theory" assuming we are talking about the
> > same thing.
>
> Sorry. I come to know category theory in Fench textbooks where its
> named "La théorie des catégories" but I know English "category
> theory" also.
>
> >
> > >
> > > The theory of categories unites object databases, relational database,
> > > functional model, NIAM. It replaces theory of sets as fundamental
> > > theory also.
> >
> > Do you mean that category theory can be used as foundations instead of
> > set theory ? That's a very controversial statement, and it would be
> > probably safe to say that the majority of mathematicians do not support
> > an idea like that.
>
> It is not controversial. Seminal works by mathematics like Mac Lane
> and Lawvere who solved the mystery of what natural number is explains
> why sets are not foundations but category theory is.
>
> >I am not sure you are qualified to make statements
> > like "It replaces theory of sets".
>
> I studied category theory at l'ENCP, l'École Nationale des Ponts et
> Chaussées, in Paris. What are you qualifications ? I think that
> you do not now lot about category theory.
>
> > Replaces how exactly ?
>
> You can read the books by Mac Lane and Lawvere or you can study your
> multiplication table that is set theory. The choice is to you. If you
> read Lawvere you can then read Zinovy Diskin who introduced category
> theory into databases.
>
>
> --
> Tegi
>
> >
> >
> > >
> > >
> > > --
> > >
> > > Tegi
> > >
Bonjour...
I am intrigued.
In what areas of RM do you exactly believe that category theory may be a better abstract mathematical tool than set theory for solving data manipulationor structuraization issues? Received on Fri Nov 03 2006 - 22:44:45 CET