@article(al2002multiple, author = {Al-Agl, F. A. and R. Brown and R. Steiner}, year = {2002}, title = {Multiple categories: the equivalence of a globular and a cubical approach}, journal = {Advances in Mathematics}, volume = {170}, number = {1}, pages = {71--118}, doi = {10.1006/aima.2001.2069}, ) @article(backens2014zx, author = {M. Backens}, year = {2014}, title = {The ZX-calculus is complete for stabilizer quantum mechanics}, journal = {New Journal of Physics}, volume = {16}, number = {9}, pages = {093021}, doi = {10.1088/1367-2630/16/9/093021}, ) @misc(bar2016globular, author = {K. Bar and A. Kissinger and J. Vicary}, title = {The \emph{Globular} proof assistant}, howpublished = {\url{http://ncatlab.org/nlab/show/Globular}}, ) @misc(batanin2002computads, author = {M. Batanin}, year = {2002}, title = {Computads and slices of operads}, url = {https://arxiv.org/abs/math/0209035}, ) @inproceedings(beck1969distributive, author = {J. Beck}, year = {1969}, title = {Distributive laws}, booktitle = {Seminar on triples and categorical homology theory}, organization = {Springer}, pages = {119--140}, doi = {10.1007/BFb0083084}, ) @book(boardman1973homotopy, author = {J. M. Boardman and R. M. Vogt}, year = {1973}, title = {Homotopy invariant algebraic structures on topological spaces}, publisher = {Springer}, doi = {10.1007/978-3-642-54830-7\_23}, ) @inproceedings(bonchi2014interacting, author = {F. Bonchi and P. Soboci{\'n}ski and F. Zanasi}, year = {2014}, title = {Interacting Bialgebras Are {F}robenius}, booktitle = {Foundations of Software Science and Computation Structures}, organization = {Springer}, pages = {351--365}, doi = {10.1007/978-3-642-54830-7\_23}, ) @article(bonchi2014hopf, author = {F. Bonchi and P. Sobocinski and F. Zanasi}, year = {2017}, title = {Interacting Hopf algebras}, journal = {Journal of Pure and Applied Algebra}, volume = {221}, number = {1}, pages = {144 -- 184}, doi = {10.1016/j.jpaa.2016.06.002}, ) @article(brown1981algebra, author = {R. Brown and P. J. Higgins}, year = {1981}, title = {On the algebra of cubes}, journal = {Journal of Pure and Applied Algebra}, volume = {21}, number = {3}, pages = {233--260}, doi = {10.1016/0022-4049(81)90018-9}, ) @article(brown1987tensor, author = {R. Brown and P. J. Higgins}, year = {1987}, title = {Tensor products and homotopies for $\omega$-groupoids and crossed complexes}, journal = {Journal of Pure and Applied Algebra}, volume = {47}, number = {1}, pages = {1--33}, doi = {10.1016/0022-4049(87)90099-5}, ) @book(brown2011nonabelian, author = {R. Brown and P. J. Higgins and R. Sivera}, year = {2011}, title = {Nonabelian algebraic topology}, publisher = {European Mathematical Society}, doi = {10.4171/083}, ) @misc(buckley2015orientals, author = {M. Buckley and R. Garner}, year = {2015}, title = {Orientals and cubes, inductively}, url = {https://arxiv.org/abs/1509.00618}, ) @article(burroni1993higher, author = {A. Burroni}, year = {1993}, title = {Higher-dimensional word problems with applications to equational logic}, journal = {Theoretical Computer Science}, volume = {115}, number = {1}, pages = {43--62}, doi = {10.1016/0304-3975(93)90054-W}, ) @incollection(coecke2008interacting, author = {B. Coecke and R. Duncan}, year = {2008}, title = {Interacting quantum observables}, booktitle = {Automata, Languages and Programming}, publisher = {Springer}, pages = {298--310}, doi = {10.1007/978-3-540-70583-3\_25}, ) @book(coecke2015picturing, author = {B. Coecke and A. Kissinger}, year = {2017}, title = {Picturing quantum processes}, publisher = {Cambridge University Press}, note = {To appear}, ) @article(crans1995pasting, author = {S. E. Crans}, year = {1995}, title = {Pasting schemes for the monoidal biclosed structure on $\omega$-Cat}, note = {Utrecht University}, ) @inproceedings(duncan2016interacting, author = {R. Duncan and K. Dunne}, year = {2016}, title = {Interacting Frobenius Algebras Are Hopf}, booktitle = {Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science}, series = {LICS '16}, pages = {535--544}, doi = {10.1145/2933575.2934550}, ) @misc(dunn2016surface, author = {L. Dunn and J. Vicary}, year = {2016}, title = {Coherence for Frobenius pseudomonoids and the geometry of linear proofs}, url = {https://arxiv.org/abs/1601.05372v3}, ) @article(eckmann1962group, author = {B. Eckmann and P. J. Hilton}, year = {1962}, title = {Group-like structures in general categories {I}: multiplications and comultiplications}, journal = {Mathematische Annalen}, volume = {145}, number = {3}, pages = {227--255}, doi = {10.1007/BF01451367}, ) @book(grandis2009directed, author = {M. Grandis}, year = {2009}, title = {Directed Algebraic Topology: Models of non-reversible worlds}, volume = {13}, publisher = {Cambridge University Press}, doi = {10.1017/CBO9780511657474}, ) @article(guiraud2006three, author = {Y. Guiraud}, year = {2006}, title = {The three dimensions of proofs}, journal = {Annals of Pure and Applied Logic}, volume = {141}, number = {1}, pages = {266--295}, doi = {10.1016/j.apal.2005.12.012}, ) @inproceedings(hadzihasanovic2015diagrammatic, author = {A. Hadzihasanovic}, year = {2015}, title = {A Diagrammatic Axiomatisation for Qubit Entanglement}, booktitle = {Logic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on}, organization = {IEEE}, pages = {573--584}, doi = {10.1109/LICS.2015.59}, ) @article(hermida2000representable, author = {C. Hermida}, year = {2000}, title = {Representable multicategories}, journal = {Advances in Mathematics}, volume = {151}, number = {2}, pages = {164--225}, doi = {10.1006/aima.1999.1877}, ) @article(hermida2001coherent, author = {C. Hermida}, year = {2001}, title = {From coherent structures to universal properties}, journal = {Journal of Pure and Applied Algebra}, volume = {165}, number = {1}, pages = {7--61}, doi = {10.1016/S0022-4049(01)00008-1}, ) @article(heunen2012lectures, author = {C. Heunen and J. Vicary}, year = {2012}, title = {Lectures on categorical quantum mechanics}, journal = {Computer Science Department. Oxford University}, ) @article(hinze2016equational, author = {R. Hinze and D. Marsden}, year = {2016}, title = {Equational reasoning with lollipops, forks, cups, caps, snakes, and speedometers}, journal = {Journal of Logical and Algebraic Methods in Programming}, doi = {10.1016/j.jlamp.2015.12.004}, ) @article(lack2004composing, author = {S. Lack}, year = {2004}, title = {Composing {PROP}s}, journal = {Theory and Applications of Categories}, volume = {13}, number = {9}, pages = {147--163}, ) @article(lafont2007algebra, author = {Y. Lafont}, year = {2007}, title = {Algebra and geometry of rewriting}, journal = {Applied Categorical Structures}, volume = {15}, number = {4}, pages = {415--437}, doi = {10.1007/s10485-007-9083-6}, ) @article(lafont2009polygraphic, author = {Y. Lafont and F. M{\'e}tayer}, year = {2009}, title = {Polygraphic resolutions and homology of monoids}, journal = {Journal of Pure and Applied Algebra}, volume = {213}, number = {6}, pages = {947--968}, doi = {10.1016/j.jpaa.2008.10.005}, ) @article(maclane1963natural, author = {S. MacLane}, year = {1963}, title = {Natural associativity and commutativity}, journal = {Rice Institute Pamphlet-Rice University Studies}, volume = {49}, number = {4}, ) @misc(makkai2001comparing, author = {M. Makkai}, year = {2005}, title = {The word problem for computads}, note = {Available on the author's web page \url{http://www.math.mcgill.ca/makkai/}}, ) @article(markl2008operads, author = {M. Markl}, year = {2008}, title = {Operads and PROPS}, journal = {Handbook of Algebra}, volume = {5}, pages = {87--140}, doi = {10.1016/S1570-7954(07)05002-4}, ) @book(markl2007operads, author = {M. Markl and S. Shnider and J. D. Stasheff}, year = {2007}, title = {Operads in algebra, topology and physics}, volume = {96}, publisher = {American Mathematical Soc.}, doi = {10.1090/surv/096}, ) @article(metayer2003resolutions, author = {F. M{\'e}tayer}, year = {2003}, title = {Resolutions by polygraphs}, journal = {Theory and Applications of Categories}, volume = {11}, number = {7}, pages = {148--184}, ) @misc(mimram2014towards, author = {S. Mimram}, year = {2014}, title = {Towards 3-dimensional rewriting theory}, url = {https://arxiv.org/abs/1410.2901}, ) @misc(perk2006yang, author = {J.H.H. Perk and Au-Yang, H.}, year = {2006}, title = {Yang-{B}axter equations}, url = {https://arxiv.org/abs/math-ph/0606053}, ) @article(selinger2011finite, author = {P. Selinger}, year = {2011}, title = {Finite dimensional Hilbert spaces are complete for dagger compact closed categories}, journal = {Electronic Notes in Theoretical Computer Science}, volume = {270}, number = {1}, pages = {113--119}, doi = {10.1016/j.entcs.2011.01.010}, ) @incollection(selinger2011survey, author = {P. Selinger}, year = {2011}, title = {A survey of graphical languages for monoidal categories}, booktitle = {New structures for physics}, publisher = {Springer}, pages = {289--355}, ) @article(steiner2004omega, author = {R. Steiner}, year = {2004}, title = {Omega-categories and chain complexes}, journal = {Homology, Homotopy and Applications}, volume = {6}, number = {1}, pages = {175--200}, doi = {10.4310/HHA.2004.v6.n1.a12}, ) @article(street1976limits, author = {R. Street}, year = {1976}, title = {Limits indexed by category-valued 2-functors}, journal = {Journal of Pure and Applied Algebra}, volume = {8}, number = {2}, pages = {149--181}, doi = {10.1016/0022-4049(76)90013-X}, ) @article(street1987algebra, author = {R. Street}, year = {1987}, title = {The algebra of oriented simplexes}, journal = {Journal of Pure and Applied Algebra}, volume = {49}, number = {3}, pages = {283--335}, doi = {10.1016/0022-4049(87)90137-X}, ) @misc(tubella2016subatomic, author = {A. A. Tubella and A. Guglielmi}, year = {2016}, title = {Subatomic Proof Systems}, note = {Available on the author's web page \url{http://alessio.guglielmi.name/res/cos/}}, ) @article(weiss2011operads, author = {I. Weiss}, year = {2011}, title = {From operads to dendroidal sets}, journal = {Mathematical foundations of quantum field theory and perturbative string theory}, volume = {83}, pages = {31--70}, doi = {10.1090/pspum/083/2742425}, ) @misc(zeng2015abstract, author = {W. Zeng}, year = {2015}, title = {The Abstract Structure of Quantum Algorithms}, url = {https://arxiv.org/abs/1512.08062}, )