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

Cimode wrote:
> 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?

See NIAM conceptual data modelling for example in http://citeseer.ist.psu.edu/cache/papers/cs/729/ftp:zSzzSzftp.cs.kun.nlzSzpubzSzSoftwEng.InfSystzSzarticleszSzCTPerspective.pdf/terhofstede96conceptual.pdf

and

P Lyngbaek and V. Vianu. Mapping a semantic database model to the relational model

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Tegi