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

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



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> > Tegi

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