維基百科

應用範疇論

應用範疇論係一門學術，專係研究點樣將範疇論嘅唔同方法套用喺其他學科[1][2][3]，譬如電腦科學[4][5]、物理（尤其係量子力學[6][7][8]）、控制理論[9][10]、自然語言處理[11][12]、概率論同埋因果律。範疇論喺呢啲範疇嘅應用可以有唔同嘅形式嘅，有啲情況會係將某個領域形式化做範疇論嘅語言，噉樣嚟到特出呢個領域入面嘅重要結構同特徵。喺其他情況呢，呢種形式化就可以透過抽象化呢種方法嚟到喺個領域入面證明到啲新嘅結果。

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  1. ↑ "Applied Category Theory". MIT OpenCourseWare. 喺2019-07-20搵到.
  2. ↑ Spivak, David I.; Fong, Brendan (July 2019). An Invitation to Applied Category Theory by Brendan Fong. doi:10.1017/9781108668804. ISBN 9781108668804.
  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. (2017-03-16). Picturing quantum processes : a first course in quantum theory and diagrammatic reasoning. ISBN 978-1107104228. OCLC 1026174191.
  9. ↑ Master, Jade; Baez, John C. (2018-08-16). "Open Petri Nets". arXiv:1808.05415v4 [math.CT].
  10. ↑ 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.
  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

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  1. ↑ "The n-Category Café". golem.ph.utexas.edu. 喺2019-07-20搵到.
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