{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T09:13:47Z","timestamp":1743153227737,"version":"3.40.3"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319403694"},{"type":"electronic","value":"9783319403700"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-40370-0_3","type":"book-chapter","created":{"date-parts":[[2016,6,3]],"date-time":"2016-06-03T09:50:55Z","timestamp":1464947455000},"page":"11-32","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lawvere Categories as Composed PROPs"],"prefix":"10.1007","author":[{"given":"Filippo","family":"Bonchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pawel","family":"Sobocinski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabio","family":"Zanasi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,4]]},"reference":[{"key":"3_CR1","unstructured":"Baez, J.C., Erbele, J.: Categories in control (2014). CoRR abs\/1405.6881"},{"key":"3_CR2","unstructured":"Baez, J.C.: Universal algebra and diagrammatic reasoning. Lecture (2006). \n                    http:\/\/math.ucr.edu\/home\/baez\/universal\/universal_hyper.pdf"},{"key":"3_CR3","series-title":"Lecture Notes in Applied and Computational Mechanics","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-01100-9_1","volume-title":"Numerics of Unilateral Contacts and Friction","author":"C Studer","year":"2009","unstructured":"Studer, C.: Introduction. In: Studer, C. (ed.) Numerics of Unilateral Contacts and Friction. LNACM, vol. 47, pp. 1\u20138. Springer, Heidelberg (2009)"},{"key":"3_CR4","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.tcs.2015.03.024","volume":"604","author":"F Bonchi","year":"2015","unstructured":"Bonchi, F., Milius, S., Silva, A., Zanasi, F.: Killing epsilons with a dagger \u2013 a coalgebraic study of systems with algebraic label structure. Theoret. Comput. Sci. 604, 102\u2013126 (2015)","journal-title":"Theoret. Comput. Sci."},{"key":"3_CR5","series-title":"Lecture notes in computer science","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/978-3-662-44584-6_30","volume-title":"CONCUR 2014 \u2013 Concurrency Theory","author":"F Bonchi","year":"2014","unstructured":"Bonchi, F., Soboci\u0144ski, P., Zanasi, F.: A categorical semantics of signal flow graphs. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 435\u2013450. Springer, Heidelberg (2014)"},{"key":"3_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/978-3-642-54830-7_23","volume-title":"Foundations of Software Science and Computation Structures","author":"F Bonchi","year":"2014","unstructured":"Bonchi, F., Soboci\u0144ski, P., Zanasi, F.: Interacting bialgebras are Frobenius. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 351\u2013365. Springer, Heidelberg (2014)"},{"key":"3_CR7","doi-asserted-by":"crossref","unstructured":"Bonchi, F., Sobocinski, P., Zanasi, F.: Full abstraction for signal flow graphs. In: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2015, pp. 515\u2013526 (2015)","DOI":"10.1145\/2775051.2676993"},{"issue":"1:14","key":"3_CR8","first-page":"1","volume":"11","author":"F Bonchi","year":"2015","unstructured":"Bonchi, F., Zanasi, F.: Bialgebraic semantics for logic programming. Log. Methods Comput. Sci. 11(1:14), 1\u201347 (2015)","journal-title":"Log. Methods Comput. Sci."},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-3-642-40206-7_9","volume-title":"Algebra and Coalgebra in Computer Science","author":"MM Bonsangue","year":"2013","unstructured":"Bonsangue, M.M., Hansen, H.H., Kurz, A., Rot, J.: Presenting distributive laws. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 95\u2013109. Springer, Heidelberg (2013)"},{"key":"3_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525858","volume-title":"Handbook of Categorical Algebra 1 - Basic Category Theory","author":"F Borceux","year":"1994","unstructured":"Borceux, F.: Handbook of Categorical Algebra 1 - Basic Category Theory. Cambridge Univ. Press, Cambridge (1994)"},{"key":"3_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1007\/978-3-642-23217-6_21","volume-title":"CONCUR 2011 \u2013 Concurrency Theory","author":"R Bruni","year":"2011","unstructured":"Bruni, R., Melgratti, H., Montanari, U.: A connector algebra for P\/T nets interactions. In: Katoen, J.-P., K\u00f6nig, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 312\u2013326. Springer, Heidelberg (2011)"},{"issue":"3\u20134","key":"3_CR12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.3233\/FI-2014-1103","volume":"134","author":"R Bruni","year":"2014","unstructured":"Bruni, R., Montanari, U., Plotkin, G.D., Terreni, D.: On hierarchical graphs: reconciling bigraphs, gs-monoidal theories and gs-graphs. Fundam. Inform. 134(3\u20134), 287\u2013317 (2014)","journal-title":"Fundam. Inform."},{"key":"3_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3","volume-title":"A Course in Universal Algebra","author":"S Burris","year":"1981","unstructured":"Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra. Springer, Heidelberg (1981)"},{"key":"3_CR14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0304-3975(93)90054-W","volume":"115","author":"A Burroni","year":"1993","unstructured":"Burroni, A.: Higher dimensional word problems with applications to equational logic. Theor. Comput. Sci. 115, 43\u201362 (1993)","journal-title":"Theor. Comput. Sci."},{"issue":"4","key":"3_CR15","doi-asserted-by":"publisher","first-page":"043016","DOI":"10.1088\/1367-2630\/13\/4\/043016","volume":"13","author":"B Coecke","year":"2011","unstructured":"Coecke, B., Duncan, R.: Interacting quantum observables: categorical algebra and diagrammatics. New J. Phys. 13(4), 043016 (2011)","journal-title":"New J. Phys."},{"issue":"4","key":"3_CR16","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1023\/A:1008647417502","volume":"7","author":"A Corradini","year":"1999","unstructured":"Corradini, A., Gadducci, F.: An algebraic presentation of term graphs, via gs-monoidal categories. Appl. Categorical Struct. 7(4), 299\u2013331 (1999)","journal-title":"Appl. Categorical Struct."},{"key":"3_CR17","volume-title":"Hopf Algebras, Pure and Applied Mathematics","author":"S Dascalescu","year":"2001","unstructured":"Dascalescu, S., Nastasescu, C., Raianu, S.: Hopf Algebras, Pure and Applied Mathematics, vol. 235. Marcel Dekker Inc., New York (2001). An Introduction"},{"key":"3_CR18","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/978-3-642-99902-4_22","volume-title":"Proceedings of the Conference on Categorical Algebra","author":"S Eilenberg","year":"1966","unstructured":"Eilenberg, S., Kelly, G.M.: Closed categories. In: Eilenberg, S., Harrison, D.K., MacLane, S., R\u00f6hri, H. (eds.) Proceedings of the Conference on Categorical Algebra, pp. 421\u2013562. Springer, Heidelberg (1966)"},{"key":"3_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/978-3-642-38164-5_4","volume-title":"Computation, Logic, Games, and Quantum Foundations","author":"M Fiore","year":"2013","unstructured":"Fiore, M., Devesas Campos, M.: The algebra of directed acyclic graphs. In: Coecke, B., Ong, L., Panangaden, P. (eds.) Computation, Logic, Games and Quantum Foundations. LNCS, vol. 7860, pp. 37\u201351. Springer, Heidelberg (2013)"},{"key":"3_CR20","unstructured":"Fong, B., Rapisarda, P., Soboci\u0144ski, P.: A categorical approach to open and interconnected dynamical systems (2015). CoRR\/1510.05076"},{"key":"3_CR21","unstructured":"Fritz, T.: A presentation of the category of stochastic matrices (2009). CoRR abs\/0902.2554. \n                    http:\/\/arxiv.org\/abs\/0902.2554"},{"issue":"1\u20133","key":"3_CR22","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.tcs.2006.03.013","volume":"357","author":"M Hyland","year":"2006","unstructured":"Hyland, M., Plotkin, G., Power, J.: Combining effects: sum and tensor. Theor. Comput. Sci. 357(1\u20133), 70\u201399 (2006)","journal-title":"Theor. Comput. Sci."},{"key":"3_CR23","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.entcs.2007.02.019","volume":"172","author":"M Hyland","year":"2007","unstructured":"Hyland, M., Power, J.: The category theoretic understanding of universal algebra: Lawvere theories and monads. Electron. Notes Theor. Comput. Sci. 172, 437\u2013458 (2007)","journal-title":"Electron. Notes Theor. Comput. Sci."},{"issue":"1","key":"3_CR24","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0168-0072(94)90020-5","volume":"69","author":"B Jacobs","year":"1994","unstructured":"Jacobs, B.: Semantics of weakening and contraction. Ann. Pure Appl. Logic 69(1), 73\u2013106 (1994)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"9","key":"3_CR25","first-page":"147","volume":"13","author":"S Lack","year":"2004","unstructured":"Lack, S.: Composing PROPs. Theor. App. Categories 13(9), 147\u2013163 (2004)","journal-title":"Theor. App. Categories"},{"key":"3_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/3-540-59340-3_13","volume-title":"Term Rewriting","author":"Y Lafont","year":"1995","unstructured":"Lafont, Y.: Equational reasoning with 2-dimensional diagrams. Term Rewriting. LNCS, vol. 909, pp. 170\u2013195. Springer, Heidelberg (1995)"},{"key":"3_CR27","unstructured":"Lawvere, W.F.: Functorial semantics of algebraic theories. Ph.D. thesis (2004)"},{"key":"3_CR28","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1090\/S0002-9904-1965-11234-4","volume":"71","author":"S Mac Lane","year":"1965","unstructured":"Mac Lane, S.: Categorical algebra. Bull. Am. Math. Soc. 71, 40\u2013106 (1965)","journal-title":"Bull. Am. Math. Soc."},{"key":"3_CR29","volume-title":"Categories for the Working Mathematician","author":"S Mac Lane","year":"1998","unstructured":"Mac Lane, S.: Categories for the Working Mathematician. Springer, Heidelberg (1998)"},{"key":"3_CR30","unstructured":"Melli\u00e8s, P.A.: Categorical semantics of linear logic. In: Interactive Models of Computation and Program Behaviour, Panoramas et Synth\u00e8ses 27, Soci\u00e9t\u00e9 Math\u00e9matique de France 1196 (2009)"},{"issue":"13","key":"3_CR31","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/S0022-4049(02)00140-8","volume":"175","author":"R Rosebrugh","year":"2002","unstructured":"Rosebrugh, R., Wood, R.: Distributive laws and factorization. J. Pure Appl. Algebra 175(13), 327\u2013353 (2002). Special Volume celebrating the 70th birthday of Professor Max Kelly","journal-title":"J. Pure Appl. Algebra"},{"key":"3_CR32","unstructured":"Ross Duncan, K.D.: Interacting Frobenius algebras are Hopf. CoRR abs\/1601.04964 (2016). \n                    http:\/\/arxiv.org\/abs\/1601.04964"},{"issue":"813","key":"3_CR33","first-page":"289","volume":"13","author":"P Selinger","year":"2011","unstructured":"Selinger, P.: A survey of graphical languages for monoidal categories. Springer Lect. Notes Phys. 13(813), 289\u2013355 (2011)","journal-title":"Springer Lect. Notes Phys."},{"volume-title":"Term Graph Rewriting: Theory and Practice","year":"1993","key":"3_CR34","unstructured":"Sleep, M.R., Plasmeijer, M.J., van Eekelen, M.C.J.D. (eds.): Term Graph Rewriting: Theory and Practice. Wiley, Chichester (1993)"},{"key":"3_CR35","doi-asserted-by":"crossref","unstructured":"Soboci\u0144ski, P., Stephens, O.: A programming language for spatial distribution of net systems. In: Petri Nets 2014 (2014)","DOI":"10.1007\/978-3-319-07734-5_9"},{"issue":"1","key":"3_CR36","first-page":"243","volume":"2","author":"R Street","year":"2002","unstructured":"Street, R.: The formal theory of monads. J. Pure Appl. Algebra 2(1), 243\u2013265 (2002)","journal-title":"J. Pure Appl. Algebra"},{"key":"3_CR37","unstructured":"Zanasi, F.: Interacting Hopf algebras: the theory of linear systems. Ph.D. thesis, Ecole Normale Sup\u00e9rieure de Lyon (2015)"}],"container-title":["Lecture Notes in Computer Science","Coalgebraic Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-40370-0_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T00:03:28Z","timestamp":1591142608000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-40370-0_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319403694","9783319403700"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-40370-0_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"4 June 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}