@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},
)