{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T18:31:22Z","timestamp":1781893882514,"version":"3.54.5"},"publisher-location":"New York, NY, USA","reference-count":35,"publisher":"ACM","license":[{"start":{"date-parts":[[2016,7,5]],"date-time":"2016-07-05T00:00:00Z","timestamp":1467676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2016,7,5]]},"DOI":"10.1145\/2933575.2934550","type":"proceedings-article","created":{"date-parts":[[2016,10,14]],"date-time":"2016-10-14T13:34:47Z","timestamp":1476452087000},"page":"535-544","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Interacting Frobenius Algebras are Hopf"],"prefix":"10.1145","author":[{"given":"Ross","family":"Duncan","sequence":"first","affiliation":[{"name":"University of Strathclyde, Glasgow, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Dunne","sequence":"additional","affiliation":[{"name":"University of Strathclyde, Glasgow, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,7,5]]},"reference":[{"key":"e_1_3_2_1_1_1","first-page":"0808","article-title":"Categorical quantum mechanics","author":"Abramsky Samson","year":"2008","unstructured":"Samson Abramsky and Bob Coecke . Categorical quantum mechanics . In Handbook of Quantum Logic and Quantum Structures , volume II . Elsevier, 2008 , arXiv: 0808 .1023. Samson Abramsky and Bob Coecke. Categorical quantum mechanics. In Handbook of Quantum Logic and Quantum Structures, volume II. Elsevier, 2008, arXiv:0808.1023.","journal-title":"Handbook of Quantum Logic and Quantum Structures"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-008-9393-1"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/16\/9\/093021"},{"key":"e_1_3_2_1_4_1","first-page":"1507","article-title":"Making the stabilizer zx-calculus complete for scalars","volume":"2015","author":"Backens Miriam","year":"2015","unstructured":"Miriam Backens . Making the stabilizer zx-calculus complete for scalars . In QPL 2015 , 2015 , arXiv: 1507 .03854. Miriam Backens. Making the stabilizer zx-calculus complete for scalars. In QPL 2015, 2015, arXiv:1507.03854.","journal-title":"QPL"},{"key":"e_1_3_2_1_5_1","first-page":"1","volume-title":"Foundations of Physics","author":"Backens Miriam","year":"2015","unstructured":"Miriam Backens and Ali Nabi Duman . A complete graphical calculus for Spekkens' toy bit theory . Foundations of Physics , pages 1 -- 34 , 2015 , arXiv:1411.1618. Miriam Backens and Ali Nabi Duman. A complete graphical calculus for Spekkens' toy bit theory. Foundations of Physics, pages 1--34, 2015, arXiv:1411.1618."},{"key":"e_1_3_2_1_6_1","volume-title":"Baez and Jason Erbele. Categories in control. arXiv.org, (1405.6881)","author":"John","year":"2014","unstructured":"John C. Baez and Jason Erbele. Categories in control. arXiv.org, (1405.6881) , 2014 , arXiv:1405.6881. John C. Baez and Jason Erbele. Categories in control. arXiv.org, (1405.6881), 2014, arXiv:1405.6881."},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/645735.666113"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-54830-7_23"},{"key":"e_1_3_2_1_9_1","volume-title":"Interacting Hopf algebras. Technical report, arXiv:1403.7048","author":"Bonchi F.","year":"2014","unstructured":"F. Bonchi , P. Soboci\u0144ski , and F. Zanasi . Interacting Hopf algebras. Technical report, arXiv:1403.7048 , 2014 . F. Bonchi, P. Soboci\u0144ski, and F. Zanasi. Interacting Hopf algebras. Technical report, arXiv:1403.7048, 2014."},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44584-6_30"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/2040235.2040263"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004110000599"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70583-3_25"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2008.04.015"},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129512000047"},{"issue":"043016","key":"e_1_3_2_1_16_1","first-page":"0906","article-title":"Interacting quantum observables: Categorical algebra and diagrammatics","volume":"13","author":"Coecke Bob","year":"2011","unstructured":"Bob Coecke and Ross Duncan . Interacting quantum observables: Categorical algebra and diagrammatics . New J. Phys , 13 ( 043016 ), 2011 , arXiv: 0906 .4725. Bob Coecke and Ross Duncan. Interacting quantum observables: Categorical algebra and diagrammatics. New J. Phys, 13(043016), 2011, arXiv:0906.4725.","journal-title":"New J. Phys"},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2012.35"},{"key":"e_1_3_2_1_18_1","series-title":"Electronic Proceedings in Theoretical Computer Science","first-page":"33","volume-title":"Proc.QPL","author":"Duncan Ross","year":"2013","unstructured":"Ross Duncan and Maxime Lucas . Verifying the Steane code with Quantomatic . In Proc.QPL 2013 , volume 171 of Electronic Proceedings in Theoretical Computer Science , pages 33 -- 49 , 2014, arXiv:1306.4532. Ross Duncan and Maxime Lucas. Verifying the Steane code with Quantomatic. In Proc.QPL 2013, volume 171 of Electronic Proceedings in Theoretical Computer Science, pages 33--49, 2014, arXiv:1306.4532."},{"key":"e_1_3_2_1_19_1","series-title":"Electronic Proceedings in Theoretical Computer Science","first-page":"50","volume-title":"Proc. QPL","author":"Duncan Ross","year":"2013","unstructured":"Ross Duncan and Simon Perdrix . Pivoting makes the zx-calculus complete for real stabilizers . In Proc. QPL 2013 , volume 171 of Electronic Proceedings in Theoretical Computer Science , pages 50 -- 62 . Open Publishing Association , 2014, arXiv:1307.7048. Ross Duncan and Simon Perdrix. Pivoting makes the zx-calculus complete for real stabilizers. In Proc. QPL 2013, volume 171 of Electronic Proceedings in Theoretical Computer Science, pages 50--62. Open Publishing Association, 2014, arXiv:1307.7048."},{"key":"e_1_3_2_1_21_1","volume-title":"Diagrammatic Discourse","author":"Fauser Bertfried","year":"2013","unstructured":"Bertfried Fauser . Some graphical aspects of Frobenius algebras. In Quantum Physics and Linguistics: A Compositional , Diagrammatic Discourse . Oxford , 2013 , arXiv:1202.6380. Bertfried Fauser. Some graphical aspects of Frobenius algebras. In Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse. Oxford, 2013, arXiv:1202.6380."},{"key":"e_1_3_2_1_22_1","volume-title":"Fourier transforms from strongly complementary observables. Sumbitted to Applied Categorical Structures","author":"Gogioso Stefano","year":"2015","unstructured":"Stefano Gogioso and William Zeng . Fourier transforms from strongly complementary observables. Sumbitted to Applied Categorical Structures , 2015 , arXiv:1501.04995. Stefano Gogioso and William Zeng. Fourier transforms from strongly complementary observables. Sumbitted to Applied Categorical Structures, 2015, arXiv:1501.04995."},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(80)90101-2"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511615443","volume-title":"Frobenius Algebras and 2-D Topological Quantum Field Theories","author":"Kock J.","year":"2003","unstructured":"J. Kock . Frobenius Algebras and 2-D Topological Quantum Field Theories . Cambridge University Press , 2003 . J. Kock. Frobenius Algebras and 2-D Topological Quantum Field Theories. Cambridge University Press, 2003."},{"issue":"9","key":"e_1_3_2_1_25_1","first-page":"147","volume":"13","author":"Lack Stephen","year":"2004","unstructured":"Stephen Lack . Composing PRO Ps . Theory and Applications of Categories , 13 ( 9 ): 147 -- 163 , 2004 , https:\/\/2.zoppoz.workers.dev:443\/http\/www.tac.mta.ca\/tac\/volumes\/13\/9\/13-09abs.html. Stephen Lack. Composing PROPs. Theory and Applications of Categories, 13(9):147--163, 2004, https:\/\/2.zoppoz.workers.dev:443\/http\/www.tac.mta.ca\/tac\/volumes\/13\/9\/13-09abs.html.","journal-title":"Theory and Applications of Categories"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2009.19"},{"key":"e_1_3_2_1_27_1","volume-title":"The ZX calculus is incomplete for Clifford+T quantum mechanics. arXiv.org","author":"Perdrix Simon","year":"2015","unstructured":"Simon Perdrix and Quanlong Wang . The ZX calculus is incomplete for Clifford+T quantum mechanics. arXiv.org , 2015 , arXiv:1506.03055. Simon Perdrix and Quanlong Wang. The ZX calculus is incomplete for Clifford+T quantum mechanics. arXiv.org, 2015, arXiv:1506.03055."},{"key":"e_1_3_2_1_28_1","volume-title":"Theory and Applications of Categories (Special Issue for CT2004)","author":"Rosebrugh R.","year":"2005","unstructured":"R. Rosebrugh , N. Sabadini , and R.F.C. Walters . Generic commutative separable algebras and cospans of graphs . Theory and Applications of Categories (Special Issue for CT2004) , 15(6):164--177, 2005 . R. Rosebrugh, N. Sabadini, and R.F.C. Walters. Generic commutative separable algebras and cospans of graphs. Theory and Applications of Categories (Special Issue for CT2004), 15(6):164--177, 2005."},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/ext044"},{"key":"e_1_3_2_1_30_1","volume-title":"Journal of Logic and Computation","author":"Sadrzadeh Mehrnoosh","year":"2014","unstructured":"Mehrnoosh Sadrzadeh , Stephen Clark , and Bob Coecke . The Frobenius anatomy of word meanings ii: possessive relative pronouns . Journal of Logic and Computation , 2014 . Mehrnoosh Sadrzadeh, Stephen Clark, and Bob Coecke. The Frobenius anatomy of word meanings ii: possessive relative pronouns. Journal of Logic and Computation, 2014."},{"key":"e_1_3_2_1_31_1","volume-title":"Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010)","author":"Selinger P.","year":"2010","unstructured":"P. Selinger . Autonomous categories in which A ≅ A* . In Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010) , 2010 . P. Selinger. Autonomous categories in which A ≅ A*. In Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010), 2010."},{"key":"e_1_3_2_1_32_1","series-title":"Lecture Notes in Physics","first-page":"289","volume-title":"New structures for physics","author":"Selinger Peter","year":"2011","unstructured":"Peter Selinger . A survey of graphical languages for monoidal categories . In New structures for physics , volume 813 of Lecture Notes in Physics , pages 289 -- 355 . Springer , 2011 , arXiv:0908.3347. Peter Selinger. A survey of graphical languages for monoidal categories. In New structures for physics, volume 813 of Lecture Notes in Physics, pages 289--355. Springer, 2011, arXiv:0908.3347."},{"key":"e_1_3_2_1_33_1","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1007\/978-3-642-40206-7_21","volume-title":"Algebra and Coalgebra in Computer Science","author":"Soboci\u0144ski Pawe\u0142","year":"2013","unstructured":"Pawe\u0142 Soboci\u0144ski . Nets , relations and linking diagrams . In Algebra and Coalgebra in Computer Science , volume 8089 of LNCS , pages 282 -- 298 . Springer Berlin Heidelberg , 2013 . Pawe\u0142 Soboci\u0144ski. Nets, relations and linking diagrams. In Algebra and Coalgebra in Computer Science, volume 8089 of LNCS, pages 282--298. Springer Berlin Heidelberg, 2013."},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618505","volume-title":"Quantum Groups: A Path to Current Algebra","author":"Street R.","year":"2007","unstructured":"R. Street . Quantum Groups: A Path to Current Algebra . Australian Mathematical Society Lecture Series. Cambridge University Press , 2007 . R. Street. Quantum Groups: A Path to Current Algebra. Australian Mathematical Society Lecture Series. Cambridge University Press, 2007."},{"key":"e_1_3_2_1_35_1","unstructured":"Moss E. Sweedler. Hopf Algebras. W. A. Benjamin Inc. 1969.  Moss E. Sweedler. Hopf Algebras. W. A. Benjamin Inc. 1969."},{"key":"e_1_3_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92687-0_31"}],"event":{"name":"LICS '16: 31st Annual ACM\/IEEE Symposium on Logic in Computer Science","location":"New York NY USA","acronym":"LICS '16","sponsor":["SIGLOG ACM Special Interest Group on Logic and Computation","EACSL European Association for Computer Science Logic","IEEE-CS\\DATC IEEE Computer Society"]},"container-title":["Proceedings of the 31st Annual ACM\/IEEE Symposium on Logic in Computer Science"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/2933575.2934550","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/pdf\/10.1145\/2933575.2934550","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:54:53Z","timestamp":1750222493000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/2933575.2934550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,5]]},"references-count":35,"alternative-id":["10.1145\/2933575.2934550","10.1145\/2933575"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/2933575.2934550","relation":{},"subject":[],"published":{"date-parts":[[2016,7,5]]},"assertion":[{"value":"2016-07-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}