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Databases from finite categories (lambda-the-ultimate.org)
76 points by mpweiher on May 26, 2017 | hide | past | favorite | 10 comments



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.


Similar: DPF (Diagram Predicate Framework) http://dpf.hib.no/ A related paper: http://www.sciencedirect.com/science/article/pii/S1571066108... 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."


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


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


Oh the irony. Paper about databases that just throws a database error. http://imgur.com/a/OomMv

Cached mirror: http://webcache.googleusercontent.com/search?q=cache:C-U5bLC...


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?


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


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


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


direct link to paper, https://arxiv.org/pdf/1102.1889.pdf




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