Applied category theory

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Applied category theory is an academic discipline in which methods from category theory are used to study other fields [1] [2] [3] including but not limited to computer science, [4] [5] physics (in particular quantum mechanics [6] [7] [8] [9] ), natural language processing, [10] [11] [12] control theory, [13] [14] [15] probability theory and causality. The application of category theory in these domains can take different forms. In some cases the formalization of the domain into the language of category theory is the goal, the idea here being that this would elucidate the important structure and properties of the domain. In other cases the formalization is used to leverage the power of abstraction in order to prove new results or to devlope new algorithms about the field.

Contents

List of applied category theorists

See also

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References

  1. ↑ "Applied Category Theory". MIT OpenCourseWare. Retrieved 2019-07-20.
  2. ↑ Spivak, David I.; Fong, Brendan (July 2019). An Invitation to Applied Category Theory by Brendan Fong. doi:10.1017/9781108668804. ISBN   9781108668804. S2CID   199139551.
  3. ↑ Bradley, Tai-Danae (2018-09-16). "What is Applied Category Theory?". arXiv: 1809.05923v2 [math.CT].
  4. ↑ Barr, Michael. (1990). Category theory for computing science. Wells, Charles. New York: Prentice Hall. ISBN   0131204866. OCLC   19126000.
  5. ↑ Ehrig, Hartmut; Große-Rhode, Martin; Wolter, Uwe (1998-03-01). "Applications of Category Theory to the Area of Algebraic Specification in Computer Science". Applied Categorical Structures. 6 (1): 1–35. doi:10.1023/A:1008688122154. ISSN   1572-9095. S2CID   290074.
  6. ↑ Abramsky, Samson; Coecke, Bob (2009), "Categorical Quantum Mechanics", Handbook of Quantum Logic and Quantum Structures, Elsevier, pp. 261–323, arXiv: 0808.1023 , doi:10.1016/b978-0-444-52869-8.50010-4, ISBN   9780444528698, S2CID   692816
  7. ↑ Duncan, Ross; Coecke, Bob (2011). "Interacting Quantum Observables: Categorical Algebra and Diagrammatics". New Journal of Physics. 13 (4): 043016. arXiv: 0906.4725 . Bibcode:2011NJPh...13d3016C. doi:10.1088/1367-2630/13/4/043016. S2CID   14259278.
  8. ↑ Coecke, Bob; Kissinger, Aleks (2017-03-16). Picturing quantum processes : a first course in quantum theory and diagrammatic reasoning. ISBN   978-1107104228. OCLC   1026174191.
  9. ↑ Heunen, Chris; Vicary, Jamie (2019-11-19). Categories for Quantum Theory: An Introduction. ISBN   9780198739616.
  10. ↑ Coecke, Bob; Sadrzadeh, Mehrnoosh; Clark, Stephen (2011), Mathematical Foundations for a Compositional Distributional Model of Meaning, arXiv: 1003.4394
  11. ↑ Kartsaklis, Dimitri; Sadrzadeh, Mehrnoosh; Pulman, Stephen; Coecke, Bob (2016), "Reasoning about meaning in natural language with compact closed categories and Frobenius algebras", Logic and Algebraic Structures in Quantum Computing, Cambridge University Press, pp. 199–222, arXiv: 1401.5980 , doi:10.1017/cbo9781139519687.011, ISBN   9781139519687, S2CID   8630039
  12. ↑ Grefenstette, Edward; Sadrzadeh, Mehrnoosh; Clark, Stephen; Coecke, Bob; Pulman, Stephen (2014), "Concrete Sentence Spaces for Compositional Distributional Models of Meaning", Text, Speech and Language Technology, Springer Netherlands, pp. 71–86, arXiv: 1101.0309 , doi:10.1007/978-94-007-7284-7_5, ISBN   9789400772830, S2CID   2411818
  13. ↑ Bonchi, Filippo; Sobocinski, Pawel; Zanasi, Fabio (2021), "A Survey of Compositional Signal Flow Theory", Advancing Research in Information and Communication Technology. IFIP Advances in Information and Communication Technology, Springer, doi:10.1007/978-3-030-81701-5_2
  14. ↑ Master, Jade; Baez, John C. (2018-08-16). "Open Petri Nets". arXiv: 1808.05415v4 [math.CT].
  15. ↑ Baez, John C.; Pollard, Blake S. (2018). "A compositional framework for reaction networks". Reviews in Mathematical Physics. 29 (9): 1750028–425. arXiv: 1704.02051 . Bibcode:2017RvMaP..2950028B. doi:10.1142/S0129055X17500283. ISSN   0129-055X. S2CID   119665423.
  16. ↑ "The n-Category Café". golem.ph.utexas.edu. Retrieved 2019-07-20.


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