@article(ArbibM1980,
 author       = {Michael~A. Arbib and Ernest~G. Manes},
 year         = {1980},
 title        = {Partially additive categories and flow-diagram semantics},
 journal      = {Journal of Algebra},
 volume       = {62},
 number       = {1},
 pages        = {203--227},
 doi          = {10.1016/0021-8693(80)90212-4},
)
@article(BarnumBCLS2010,
 author       = {Howard Barnum and Jonathan Barrett and Lisa~Orloff Clark and Matthew Leifer and Robert Spekkens and Nicholas Stepanik and Alex Wilce and Robin Wilke},
 year         = {2010},
 title        = {Entropy and information causality in general probabilistic theories},
 journal      = {New Journal of Physics},
 volume       = {12},
 number       = {3},
 doi          = {10.1088/1367-2630/12/3/033024},
)
@incollection(BarnumW2016,
 author       = {Howard Barnum and Alexander Wilce},
 year         = {2016},
 title        = {Post-Classical Probability Theory},
 editor       = {G.~Chiribella and R.~W. Spekkens},
 booktitle    = {Quantum Theory: Informational Foundations and Foils},
 publisher    = {Springer},
 pages        = {367--420},
 doi          = {10.1007/978-94-017-7303-4_11},
)
@article(barrett2007information,
 author       = {Jonathan Barrett},
 year         = {2007},
 title        = {Information processing in generalized probabilistic theories},
 journal      = {Physical Review A},
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 number       = {3},
 pages        = {032304},
 doi          = {10.1103/PhysRevA.75.032304},
)
@article(BoergerK1996,
 author       = {Reinhard B{\"{o}}rger and Ralf Kemper},
 year         = {1996},
 title        = {A cogenerator for preseparated superconvex spaces},
 journal      = {Applied Categorical Structures},
 volume       = {4},
 number       = {4},
 pages        = {361--370},
 doi          = {10.1007/BF00122684},
)
@article(CassinelliL2016,
 author       = {Gianni Cassinelli and Pekka Lahti},
 year         = {2016},
 title        = {An Axiomatic Basis for Quantum Mechanics},
 journal      = {Foundations of Physics},
 volume       = {46},
 number       = {10},
 pages        = {1341--1373},
 doi          = {10.1007/s10701-016-0022-y},
)
@incollection(ChiribellaDP2015,
 author       = {Giulio Chiribella and Giacomo~Mauro D'Ariano and Paolo Perinotti},
 year         = {2015},
 title        = {Quantum from Principles},
 booktitle    = {Quantum Theory: Informational Foundations and Foils},
 publisher    = {Springer},
 pages        = {171--221},
 doi          = {10.1007/978-94-017-7303-4_6},
)
@article(chiribella2010probabilistic,
 author       = {Giulio Chiribella and D\IeC{\textquoteright}Ariano, Giacomo~Mauro and Paolo Perinotti},
 year         = {2010},
 title        = {Probabilistic theories with purification},
 journal      = {Physical Review A},
 volume       = {81},
 number       = {6},
 pages        = {062348},
 doi          = {10.1103/PhysRevA.81.062348},
)
@inproceedings(Cho2015,
 author       = {Kenta Cho},
 year         = {2015},
 title        = {Total and Partial Computation in Categorical Quantum Foundations},
 booktitle    = {12th International Workshop on Quantum Physics and Logic (QPL 2015)},
 series       = {EPTCS},
 volume       = {195},
 pages        = {116--135},
 doi          = {10.4204/EPTCS.195.9},
)
@phdthesis(Cho2019PhD,
 author       = {Kenta Cho},
 year         = {2019},
 title        = {Effectuses in Categorical Quantum Foundations},
 school       = {Radboud Unviersity Nijmegen},
 url          = {http://hdl.handle.net/2066/207521},
)
@article(cho2015introduction,
 author       = {Kenta Cho and Bart Jacobs and Bas Westerbaan and Abraham Westerbaan},
 year         = {2015},
 title        = {An Introduction to Effectus Theory},
 journal      = {arXiv preprint arXiv:1512.05813},
 url          = {https://arxiv.org/abs/1512.05813},
)
@book(DArianoCP2017,
 author       = {Giacomo~Mauro D'Ariano and Giulio Chiribella and Paolo Perinotti},
 year         = {2017},
 title        = {Quantum Theory from First Principles: An Informational Approach},
 publisher    = {Cambridge University Press},
 doi          = {10.1017/9781107338340},
)
@article(DaviesL1970,
 author       = {E.~B. Davies and J.~T. Lewis},
 year         = {1970},
 title        = {An operational approach to quantum probability},
 journal      = {Communications in Mathematical Physics},
 volume       = {17},
 number       = {3},
 pages        = {239--260},
 doi          = {10.1007/BF01647093},
)
@article(Edwards1970,
 author       = {C.~M. Edwards},
 year         = {1970},
 title        = {The operational approach to algebraic quantum theory {I}},
 journal      = {Communications in Mathematical Physics},
 volume       = {16},
 number       = {3},
 pages        = {207--230},
 doi          = {10.1007/BF01646788},
)
@article(EdwardsG1970,
 author       = {C.~M. Edwards and M.~A. Gerzon},
 year         = {1970},
 title        = {Monotone convergence in partially ordered vector spaces},
 journal      = {Annales de l'I.H.P. Physique th{\'e}orique},
 volume       = {12},
 number       = {4},
 pages        = {323--328},
 url          = {http://www.numdam.org/item/AIHPA_1970__12_4_323_0},
)
@inproceedings(moliner2017space,
 author       = {Enrique~Moliner, Pau and Chris Heunen and Sean Tull},
 year         = {2018},
 title        = {Space in Monoidal Categories},
 editor       = {Bob Coecke and Aleks Kissinger},
 booktitle    = {{\rm Proceedings 14th International Conference on} Quantum Physics and Logic, {\rm Nijmegen, The Netherlands, 3-7 July 2017}},
 series       = {Electronic Proceedings in Theoretical Computer Science},
 volume       = {266},
 publisher    = {Open Publishing Association},
 pages        = {399--410},
 doi          = {10.4204/EPTCS.266.25},
)
@article(foulis1994effect,
 author       = {David~J Foulis and Mary~K Bennett},
 year         = {1994},
 title        = {Effect algebras and unsharp quantum logics},
 journal      = {Foundations of physics},
 volume       = {24},
 number       = {10},
 pages        = {1331--1352},
 doi          = {10.1007/BF02283036},
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@incollection(FoulisG2007,
 author       = {David~J. Foulis and Richard~J. Greechie},
 year         = {2007},
 title        = {Quantum logic and partially ordered abelian groups},
 booktitle    = {Handbook of Quantum Logic and Quantum Structures: Quantum Structures},
 publisher    = {Elsevier},
 pages        = {215--283},
 doi          = {10.1016/B978-044452870-4/50028-5},
)
@phdthesis(Furber2017,
 author       = {Robert Furber},
 year         = {2017},
 title        = {Categorical Duality in Probability and Quantum Foundations},
 school       = {Radboud University Nijmegen},
 url          = {http://hdl.handle.net/2066/175862},
)
@inproceedings(Furber2018QPL,
 author       = {Robert Furber},
 year         = {2019},
 title        = {Categorical Equivalences from State-Effect Adjunctions},
 booktitle    = {15th International Conference on Quantum Physics and Logic (QPL 2018)},
 volume       = {287},
 pages        = {107--126},
 doi          = {10.4204/EPTCS.287.6},
)
@book(gillman2013rings,
 author       = {Leonard Gillman and Meyer Jerison},
 year         = {2013},
 title        = {Rings of continuous functions},
 publisher    = {Springer},
 doi          = {10.1007/978-1-4615-7819-2},
)
@article(Gudder1998,
 author       = {Stanley Gudder},
 year         = {1998},
 title        = {Morphisms, tensor products and $\sigma$-effect algebras},
 journal      = {Reports on Mathematical Physics},
 volume       = {42},
 number       = {3},
 pages        = {321--346},
 doi          = {10.1016/S0034-4877(99)80003-2},
)
@article(gudder1999convex,
 author       = {Stanley Gudder},
 year         = {1999},
 title        = {Convex structures and effect algebras},
 journal      = {International Journal of Theoretical Physics},
 volume       = {38},
 number       = {12},
 pages        = {3179--3187},
 doi          = {10.1023/A:1026678114856},
)
@article(gudder1998representation,
 author       = {Stanley Gudder and Sylvia Pulmannov{\'a}},
 year         = {1998},
 title        = {Representation theorem for convex effect algebras},
 journal      = {Commentationes Mathematicae Universitatis Carolinae},
 volume       = {39},
 number       = {4},
 pages        = {645--660},
 url          = {http://dml.cz/dmlcz/119041},
)
@article(harding2004remarks,
 author       = {John Harding},
 year         = {2004},
 title        = {Remarks on concrete orthomodular lattices},
 journal      = {International Journal of Theoretical Physics},
 volume       = {43},
 number       = {10},
 pages        = {2149--2168},
 doi          = {10.1023/B:IJTP.0000049016.83846.72},
)
@article(Jacobs2011,
 author       = {Bart Jacobs},
 year         = {2011},
 title        = {Probabilities, distribution monads, and convex categories},
 journal      = {Theoretical Computer Science},
 volume       = {412},
 number       = {28},
 pages        = {3323--3336},
 doi          = {10.1016/j.tcs.2011.04.005},
)
@article(jacobs2015new,
 author       = {Bart Jacobs},
 year         = {2015},
 title        = {New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic},
 journal      = {Logical Methods in Computer Science},
 volume       = {11},
 number       = {3},
 doi          = {10.2168/LMCS-11(3:24)2015},
)
@article(jacobs2012coreflections,
 author       = {Bart Jacobs and Jorik Mandemaker},
 year         = {2012},
 title        = {Coreflections in algebraic quantum logic},
 journal      = {Foundations of physics},
 volume       = {42},
 number       = {7},
 pages        = {932--958},
 doi          = {10.1007/s10701-012-9654-8},
)
@article(JacobsMF2016,
 author       = {Bart Jacobs and Jorik Mandemaker and Robert Furber},
 year         = {2016},
 title        = {The expectation monad in quantum foundations},
 journal      = {Information and Computation},
 volume       = {250},
 pages        = {87--114},
 doi          = {10.1016/j.ic.2016.02.009},
)
@article(jenvca2015effect,
 author       = {Jen{\v{c}}a, Gejza},
 year         = {2015},
 title        = {Effect algebras are the {Eilenberg-Moore} category for the {Kalmbach} monad},
 journal      = {Order},
 volume       = {32},
 number       = {3},
 pages        = {439--448},
 doi          = {10.1007/s11083-014-9344-6},
)
@article(KochenS1967,
 author       = {Simon Kochen and E.~P. Specker},
 year         = {1967},
 title        = {The Problem of Hidden Variables in Quantum Mechanics},
 journal      = {Journal of Mathematics and Mechanics},
 volume       = {17},
 number       = {1},
 pages        = {59--87},
 doi          = {10.1512/iumj.1968.17.17004},
)
@book(Ludwig1983,
 author       = {G{\"u}nther Ludwig},
 year         = {1983},
 title        = {Foundations of Quantum Mechanics {I}},
 publisher    = {Springer},
 doi          = {10.1007/978-3-642-86751-4},
)
@book(Ludwig1985,
 author       = {G{\"u}nther Ludwig},
 year         = {1985},
 title        = {An Axiomatic Basis for Quantum Mechanics, Volume 1: Derivation of Hilbert Space Structure},
 publisher    = {Springer},
 doi          = {10.1007/978-3-642-70029-3},
)
@book(Mackey2004,
 author       = {George~W. Mackey},
 year         = {2004},
 title        = {Mathematical Foundations of Quantum Mechanics},
 publisher    = {Dover},
 note         = {Originally published by W. A. Benjamin, 1963},
)
@book(ManesA1986,
 author       = {Ernest~G. Manes and Michael~A. Arbib},
 year         = {1986},
 title        = {Algebraic Approaches to Program Semantics},
 series       = {Monographs in Computer Science},
 publisher    = {Springer},
 doi          = {10.1007/978-1-4612-4962-7},
)
@article(Pumpluen2002,
 author       = {Dieter Pumpl{\"{u}}n},
 year         = {2002},
 title        = {The Metric Completion of Convex Sets and Modules},
 journal      = {Results in Mathematics},
 volume       = {41},
 pages        = {346--360},
 doi          = {10.1007/BF03322777},
)
@article(tull2016,
 author       = {Sean Tull},
 year         = {2016},
 title        = {Operational theories of physics as categories},
 journal      = {arXiv preprint arXiv:1602.06284},
 url          = {https://arxiv.org/abs/1602.06284},
)
@phdthesis(tull2019phdthesis,
 author       = {Sean Tull},
 year         = {2018},
 title        = {Categorical Operational Physics},
 school       = {University of Oxford},
 url          = {https://arxiv.org/abs/1902.00343},
)
@inproceedings(effectmonoids,
 author       = {Abraham Westerbaan and Bas Westerbaan and John van~de Wetering},
 year         = {2020},
 title        = {A Characterisation of Ordered Abstract Probabilities},
 booktitle    = {Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science},
 series       = {LICS \IeC{\textquoteright}20},
 publisher    = {Association for Computing Machinery},
 address      = {New York, NY, USA},
 pages        = {944\IeC{\textendash}957},
 doi          = {10.1145/3373718.3394742},
)
@phdthesis(basthesis,
 author       = {Bas Westerbaan},
 year         = {2018},
 title        = {Dagger and dilations in the category of von Neumann algebras},
 school       = {Radboud University Nijmegen},
 url          = {http://hdl.handle.net/2066/201785},
)
@mastersthesis(basmaster,
 author       = {Bas~E Westerbaan},
 year         = {2013},
 title        = {Sequential product on effect logics},
 school       = {Radboud University Nijmegen},
 note         = {Available at \url{https://www.ru.nl/publish/pages/813276/masterscriptie_bas_westerbaan.pdf}},
)
@article(Wright1972,
 author       = {J.~D.~Maitland Wright},
 year         = {1972},
 title        = {Measures with Values in a Partially Ordered Vector Space},
 journal      = {Proceedings of the London Mathematical Society},
 volume       = {s3-25},
 number       = {4},
 pages        = {675--688},
 doi          = {10.1112/plms/s3-25.4.675},
)