[Categoricaldata_announce] newbie to FQL

[David Spivak]

Hi Vit,

Thanks for the email; I'm glad you're using this tool and finding it a nice
way to get acquainted with category theory.

Your first question is a bit easier. The high-level answer is that "the
limit of an empty diagram is the terminal object". Basically since nothing
is hitting a3 or a4, the sets that Pi puts there are empty products, i.e.
terminal objects in Set. The terminal object in Set is the set with one
element. You can see this issue as a kind of generalization of the fact
that 5^0=1 because 5^0 is an empty product (multiply 5*5*5...&5, but do it
0 times) and the answer is 1.

Your second question is more involved. To answer your first question we
will try to write an FQL file that does this example and send it to you
(and the list) soon. As to your second question, given a schema S=[A   B]
consisting of just two nodes, A and B, one can make a new schema T=[A <--X
--->B] with an additional object and two additional arrows. Then one can
create a functor F: S-->T. The query pi F will put the product into X with
the foreign keys you want. See the attached FQL file.

Best regards,
David


On Tue, Jul 1, 2014 at 5:28 AM, Koksa, Vit <Vit.Koksa at honeywell.com> wrote:

>  Hello,
>
>
>
> Is there any discussion forum on FQL available, please? I didn’t find any,
> so I resort to send my e-mail to this mailing list. The FQL IDE is a very
> interesting and user-friendly tool, it enables even people without a deep
> mathematical background like me to play with categories. But I don’t see
> things, which would be obvious to the more knowledgeable people.
>
>
>
> The questions which I have currently in mind are:
>
>
>
> 1.  The FQL sample code “Query Composition” contains the query q1: S -> T
> . To see how the data migration proceeds inside this query I added these
> two instances:
>
>
>
> instance Delta_sm = delta sm I
>
> instance Pi_fm = pi fm Delta_sm
>
>
>
> What I don’t understand is why both tables a3 and a4 in Pi_fm contain a
> record, when there is no mapping to these tables of the schema A from the
> tables of the schema B in the schema mapping fm.
>
>
>
> 2. How would the example given on the slide 45 of
> http://categoricaldata.net/fql/introSlides.pdf be encoded in FQL?
>
> (SELECT title, isbn FROM book WHERE price > 100)
>
> In particular and more generally I don’t know how to migrate data from
> nodes {a, b} to nodes {a, b, aXb} where aXb is the product/join of a and b,
> while “preserving” the foreign keys from aXb elements to their constituent
> parts in a and b.
>
>
>
> With regards.
>
> Vit
>
> _______________________________________________
> Categoricaldata_announce mailing list
> Categoricaldata_announce at categoricaldata.net
> https://lists.hcoop.net/listinfo/categoricaldata_announce
>
>
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