The open-source Categorical Query Language (CQL) and integrated development environment (IDE) performs data-related tasks — such as querying, combining, migrating, and evolving databases — using category theory, a branch of mathematics that has revolutionized several areas of computer science. Open-source CQL is production-ready for single-node in-memory data processing workloads, such as integrating data for data science. It is being commercialized by Conexus AI.
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.
R. Türker, L. Zhang, M. Koutraki, and H. Sack. The Semantic Web - 16th International Conference, ESWC 2019, Portoroz, Slovenia, June 2-6, 2019, Proceedings, volume 11503 of Lecture Notes in Computer Science, page 346--362. Springer, (2019)
R. Türker, L. Zhang, M. Koutraki, and H. Sack. 49. Jahrestagung der Gesellschaft für Informatik, 50 Jahre Gesellschaft für Informatik - Informatik für Gesellschaft, INFORMATIK 2019, Kassel, Germany, September 23-26, 2019, volume P-294 of LNI, page 283--284. GI, (2019)
R. Biswas, M. Koutraki, and H. Sack. Proceedings of the EKAW 2018 Posters and Demonstrations Session co-located with 21st International Conference on Knowledge Engineering and Knowledge Management (EKAW 2018), Nancy, France, November 12-16, 2018, volume 2262 of CEUR Workshop Proceedings, page 29--32. CEUR-WS.org, (2018)
T. Mossakowski. Algebra, Meaning and Computation. Essays Dedicated to Joseph A. Goguen on the Occasion of His 65th Birthday, volume 4060 of Lecture Notes in Computer Science, page 124-149. Springer; Berlin; http://www.springer.de, (2006)
C. Barwick, and C. Schommer-Pries. (2011)cite http://arxiv.org/abs/1112.0040arxiv:1112.0040Comment: 46 pages, 2 figures. Corrections of a formatting error and addition of clearer acknowledgements.
S. Lack, and R. Street. Journal of Pure and Applied Algebra, 175 (1–3):
243 - 265(2002)Special Volume celebrating the 70th birthday of Professor Max Kelly.
J. Baez, and J. Dolan. (1997)cite http://arxiv.org/abs/q-alg/9702014arxiv:q-alg/9702014Comment: 59 pages LaTex, uses diagram.sty and auxdefs.sty macros, one encapsulated Postscript figure, also available as a compressed Postscript file at http://math.ucr.edu/home/baez/op.ps.Z or ftp://math.ucr.edu/pub/baez/op.ps.Z.
U. Fahrenberg. Foundations of Software Science and Computational Structures, volume 3441 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, (2005)
B. Toen, and G. Vezzosi. (2002)cite http://arxiv.org/abs/math/0212330arxiv:math/0212330Comment: 22 pages. Slightly enlarged. Clarified the part on homotopy types of Segal topoi.
D. Gepner, and J. Kock. (2012)cite http://arxiv.org/abs/1208.1749arxiv:1208.1749Comment: 26 pages. Comments are very welcome; v2: clarified some points in the introduction, minor expository changes, added one reference. No changes in theorems and proofs.