
Databases from finite categories - mpweiher
http://lambda-the-ultimate.org/node/5435
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roflc0ptic
Slightly off topic - at Lambda Conf right now, went to Spivak's 6 hour lecture
on category theory. Whenever they post the videos, I'd recommend it. He's an
excellent instructor.

Others mentioned that his textbook on category theory was also really good,
but I can't confirm.

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enord
Similar: DPF (Diagram Predicate Framework)
[http://dpf.hib.no/](http://dpf.hib.no/) A related paper:
[http://www.sciencedirect.com/science/article/pii/S1571066108...](http://www.sciencedirect.com/science/article/pii/S1571066108004350?via%3Dihub)
Gotta love this quip from the abstract: "In the engineering jargon, it is a
modeling language design pattern that combines mathematical rigor and
appealing graphical appearance."

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wisnesky
This line of work has been continued in the FQL project:
[http://categoricaldata.net/fql.html](http://categoricaldata.net/fql.html) .
The SQL analogy is discussed in the Relational Foundations paper there.

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runeks
(From that page) This introductory video is intelligible to even me, with
fairly little knowledge of category theory:
[https://youtu.be/fTporauBJEs](https://youtu.be/fTporauBJEs)

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tuna-piano
Oh the irony. Paper about databases that just throws a database error.
[http://imgur.com/a/OomMv](http://imgur.com/a/OomMv)

Cached mirror:
[http://webcache.googleusercontent.com/search?q=cache:C-U5bLC...](http://webcache.googleusercontent.com/search?q=cache:C-U5bLCvFIIJ:lambda-
the-ultimate.org/node/5435+&cd=1&hl=en&ct=clnk&gl=us)

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ivan_ah
This is pretty interesting. The paper basically starts by talking about
"Concept maps", or graphs of concepts and relations. These concept maps
correspond to an SQL schema, and instances of concepts and relations
correspond to table rows.

Then they go one level meta and discuss how to create "alignment mappings"
between the concepts generated by different people. This makes me think about
how math standards for different countries/school systems could be aligned.
For example, using an "alignment mapping" between math topics taught in US and
math topics taught in UK, you could repurpose a high-quality educational
content source (e.g. Khan Academy) to be used in UK schools.

But wait, there is more! The space of mappings between concept maps can also
be represented as a graph also a category, and somehow there is interesting
structure that can be used to categorize and link the alignment mappings (15+
pages that I didn't understand). I wish they had continued the SQL analogy.
What would a functor be? Is it a migration? Or an ETL script? And what is a
flow?

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jessaustin
Do you intend to say that mathematics is different from UK to USA? Do they
have integers?

~~~
ivan_ah
It's not that the math is different, but the order in which concepts are
presented.

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danidiaz
The book "Big Data Integration Theory" also uses category theory to model
database mappings: [https://www.goodreads.com/book/show/19361242-big-data-
integr...](https://www.goodreads.com/book/show/19361242-big-data-integration-
theory)

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brudgers
direct link to paper,
[https://arxiv.org/pdf/1102.1889.pdf](https://arxiv.org/pdf/1102.1889.pdf)

