@book(araki,
 author       = "Huzihiro Araki",
 year         = "1999",
 title        = "Mathematical theory of quantum fields",
 series       = "International Series of Monographs on Physics",
 volume       = "101",
 publisher    = "Oxford University Press",
 address      = "New York",
)
@article(banaschewskimulvey00b,
 author       = "Bernhard Banaschewski and Christopher J. Mulvey",
 year         = "2000",
 title        = "The spectral theory of commutative {C}*-algebras: the constructive {G}elfand-{M}azur theorem",
 journal      = "Quaestiones Mathematicae",
 volume       = "23",
 number       = "4",
 pages        = "465--488",
 doi          = "10.2989/16073600009485990",
)
@article(banaschewskimulvey00a,
 author       = "Bernhard Banaschewski and Christopher J. Mulvey",
 year         = "2000",
 title        = "The spectral theory of commutative {C}*-algebras: the constructive spectrum",
 journal      = "Quaestiones Mathematicae",
 volume       = "23",
 number       = "4",
 pages        = "425--464",
 doi          = "10.2989/16073600009485989",
)
@article(banaschewskimulvey06,
 author       = "Bernhard Banaschewski and Christopher J. Mulvey",
 year         = "2006",
 title        = "A globalisation of the {G}elfand duality theorem",
 journal      = "Annals of Pure and Applied Logic",
 volume       = "137",
 number       = "1--3",
 pages        = "62--103",
 doi          = "10.1016/j.apal.2005.05.018",
)
@article(BrunettiFredenhagenVerch,
 author       = "Romeo Brunetti and Klaus Fredenhagen and Rainer Verch",
 year         = "2003",
 title        = "The generally covariant locality principle---a new paradigm for local quantum field theory",
 journal      = "Comm. Math. Phys.",
 volume       = "237",
 number       = "1-2",
 pages        = "31--68",
 doi          = "10.1007/s00220-003-0815-7",
 note         = "Dedicated to Rudolf Haag",
)
@article(butterfieldisham2,
 author       = "Jeremy Butterfield and Chris J. Isham",
 year         = "1999",
 title        = "A topos perspective on the {K}ochen-{S}pecker theorem: {II}. Conceptual Aspects and Classical Analogues",
 journal      = "International Journal of Theoretical Physics",
 volume       = "38",
 number       = "3",
 pages        = "827--859",
 doi          = "10.1023/A:1026652817988",
)
@article(butterfieldisham4,
 author       = "Jeremy Butterfield and Chris J. Isham",
 year         = "2002",
 title        = "A topos perspective on the {K}ochen-{S}pecker theorem: {IV}. Interval Valuations",
 journal      = "International Journal of Theoretical Physics",
 volume       = "41",
 number       = "4",
 pages        = "613--639",
 doi          = "10.1023/A:1015276209768",
)
@article(CaspersHLS:IntQLnLS,
 author       = "Martijn Caspers and Chris Heunen and Nicolaas P. Landsman and Bas Spitters",
 year         = "2009",
 title        = "Intuitionistic Quantum Logic of an $n$-level System",
 journal      = "Foundations of Physics",
 volume       = "39",
 pages        = "731--759",
 doi          = "10.1007/s10701-009-9308-7",
)
@article(coquand05,
 author       = "Thierry Coquand",
 year         = "2005",
 title        = "About {S}tone's Notion of Spectrum",
 journal      = "Journal of Pure and Applied Algebra",
 volume       = "197",
 pages        = "141--158",
 doi          = "10.1016/j.jpaa.2004.08.024",
)
@article(CoquandSpitters:cstar,
 author       = "Thierry Coquand and Bas Spitters",
 year         = "2009",
 title        = "Constructive {G}elfand duality for {C}*-algebras",
 journal      = "Mathematical Proceedings of the Cambridge Philosophical Society",
 volume       = "147",
 number       = "2",
 pages        = "339--344",
 doi          = "10.1017/S0305004109002515",
 note         = "ArXiv:0808.1518",
)
@article(Coquand/Spitters:integrals-valuations,
 author       = "Thierry Coquand and Bas Spitters",
 year         = "2009",
 title        = "Integrals and Valuations",
 journal      = "Journal of Logic and Analysis",
 volume       = "1",
 number       = "3",
 pages        = "1--22",
 doi          = "10.4115/jla.2009.1.3",
)
@unpublished(Doering:2012b,
 author       = "Andreas D\"oring",
 year         = "2012",
 title        = "Flows on Generalised {G}elfand Spectra of Nonabelian Unital $C^{\ast }$-Algebras and Time Evolution of Quantum Systems",
 url          = "http://arxiv.org/abs/1212.4882",
)
@unpublished(Doering:2012a,
 author       = "Andreas D\"oring",
 year         = "2012",
 title        = "Generalised {G}elfand Spectra of Nonabelian Unital $C^{*}$-Algebras",
 url          = "http://arxiv.org/abs/1212.2613",
)
@unpublished(HardingDoering,
 author       = "Andreas D\"oring and John Harding",
 year         = "2010",
 title        = "Abelian subalgebras and the {J}ordan structure of a von {N}eumann algebra",
 url          = "http://arxiv.org/abs/1009.4945",
)
@incollection(DoeringIsham:WhatThingTTFP,
 author       = "Andreas D\"{o}ring and Chris Isham",
 year         = "2011",
 title        = "`{W}hat is a {T}hing?': Topos Theory in the Foundations of Physics",
 editor       = "Bob Coecke",
 booktitle    = "New Structures in Physics",
 chapter      = "13",
 series       = "Lecture Notes in Physics",
 volume       = "813",
 publisher    = "Springer",
 pages        = "753--940",
 doi          = "10.1007/978-3-642-12821-9\_13",
 note         = "ArXiv:0803.0417",
)
@inproceedings(FRV:Born,
 author       = "Bertfried Fauser and Guillaume Raynaud and Steven Vickers",
 year         = "2012",
 title        = "The {B}orn Rule as Structure of Spectral Bundles",
 editor       = "Bart Jacobs and Peter Selinger and Bas Spitters",
 booktitle    = "Proceedings of the 8th International Workshop on Quantum Physics and Logic, {N}ijmegen 2011",
 series       = "EPTCS",
 volume       = "95",
 pages        = "81--90",
 doi          = "10.4204/EPTCS.95.8",
)
@book(Haag:LQP,
 author       = "Rudolf Haag",
 year         = "1996",
 title        = "Local Quantum Physics: Fields, Particles, Algebras",
 edition      = "second",
 series       = "Texts and Monographs in Physics",
 publisher    = "Springer-Verlag",
 address      = "Berlin",
 doi          = "10.1007/978-3-642-61458-3",
)
@article(Hamhalter:iso-order,
 author       = "Jan Hamhalter",
 year         = "2011",
 title        = "Isomorphisms of ordered structures of abelian $C^{\begingroup \let \relax \relax \endgroup [Pleaseinsert\PrerenderUnicode{∗}intopreamble]}$-subalgebras of $C^{\begingroup \let \relax \relax \endgroup [Pleaseinsert\PrerenderUnicode{∗}intopreamble]}$-algebras",
 journal      = "J. Math. Anal. Appl.",
 volume       = "383",
 pages        = "391--399",
 doi          = "10.1016/j.jmaa.2011.05.035",
)
@article(HamhalterTurilova,
 author       = "Jan Hamhalter and Ekaterina Turilova",
 year         = "2013",
 title        = "Structure of associative subalgebras of {J}ordan operator algebras",
 journal      = "The Quarterly Journal of Mathematics",
 volume       = "64",
 number       = "2",
 pages        = "397--408",
 doi          = "10.1093/qmath/has015",
)
@article(butterfieldisham3,
 author       = "John Hamilton and Chris J. Isham and Jeremy Butterfield",
 year         = "2000",
 title        = "A topos perspective on the {K}ochen-{S}pecker theorem: {III}. {V}on {N}eumann Algebras as the Base Category",
 journal      = "International Journal of Theoretical Physics",
 volume       = "39",
 number       = "6",
 pages        = "1413--1436",
 doi          = "10.1023/A:1003667607842",
)
@article(qtopos,
 author       = "Chris Heunen and Klaas Landsman and Bas Spitters",
 year         = "2009",
 title        = "A topos for algebraic quantum theory",
 journal      = "Communications in mathematical physics",
 volume       = "291",
 number       = "1",
 pages        = "63--110",
 doi          = "10.1007/s00220-009-0865-6",
 note         = "ArXiv:0709.4364",
)
@incollection(Bohrification,
 author       = "Chris Heunen and Nicolaas P. Landsman and Bas Spitters",
 year         = "2011",
 title        = "Bohrification",
 editor       = "Hans Halvorson",
 booktitle    = "Deep Beauty",
 publisher    = "Cambridge University Press",
 pages        = "271--313",
 doi          = "10.1017/CBO9780511976971.008",
 note         = "ArXiv:0909.3468",
)
@article(Bohrification_ql,
 author       = "Chris Heunen and Nicolaas P. Landsman and Bas Spitters",
 year         = "2012",
 title        = "Bohrification of operator algebras and quantum logic",
 journal      = "Synthese",
 volume       = "186",
 pages        = "719--752",
 doi          = "10.1007/s11229-011-9918-4",
)
@inproceedings(Hyl81,
 author       = "J.M.E. Hyland",
 year         = "1981",
 title        = "Function Spaces in the Category of Locales",
 editor       = "B. Banaschewski and R.-E. Hoffmann",
 booktitle    = "Continuous Lattices: Proceedings, Bremen, 1979",
 series       = "Lecture Notes in Mathematics",
 volume       = "871",
 publisher    = "Springer-Verlag",
 pages        = "264--281",
 doi          = "10.1007/BFb0089910",
)
@article(butterfieldisham1,
 author       = "Chris J. Isham and Jeremy Butterfield",
 year         = "1998",
 title        = "A topos perspective on the {K}ochen-{S}pecker theorem: {I}. Quantum States as Generalized Valuations",
 journal      = "International Journal of Theoretical Physics",
 volume       = "37",
 number       = "11",
 pages        = "2669--2733",
 doi          = "10.1023/A:1026680806775",
)
@book(James:FibrewiseTop,
 author       = "I.M. James",
 year         = "1989",
 title        = "Fibrewise Topology",
 series       = "Cambridge Tracts in Mathematics",
 volume       = "91",
 publisher    = "Cambridge University Press",
 address      = "Cambridge",
 doi          = "10.1017/CBO9780511896835",
)
@inproceedings(johnstoneloc,
 author       = "Peter T. Johnstone",
 year         = "1984",
 title        = "Open locales and exponentiation",
 editor       = "J.W. Gray",
 booktitle    = "Mathematical Applications of Category Theory",
 series       = "Contemporary Mathematics",
 volume       = "30",
 publisher    = "American Mathematical Society",
 pages        = "84--116",
 doi          = "10.1090/conm/030/749770",
)
@article(Johnstone/Joyal,
 author       = "Peter T. Johnstone and Andr\'e Joyal",
 year         = "1982",
 title        = "Continuous categories and exponentiable toposes",
 journal      = "Journal of Pure and Applied Algebra",
 volume       = "25",
 number       = "3",
 pages        = "255--296",
 doi          = "10.1016/0022-4049(82)90083-4",
)
@book(StoneSp,
 author       = "P.T. Johnstone",
 year         = "1982",
 title        = "Stone Spaces",
 series       = "Cambridge Studies in Advanced Mathematics",
 volume       = "3",
 publisher    = "Cambridge University Press",
)
@book(Elephant1,
 author       = "P.T. Johnstone",
 year         = "2002",
 title        = "Sketches of an Elephant: A Topos Theory Compendium, vol. 1",
 series       = "Oxford Logic Guides",
 volume       = "44",
 publisher    = "Oxford University Press",
)
@book(Elephant2,
 author       = "P.T. Johnstone",
 year         = "2002",
 title        = "Sketches of an Elephant: A Topos Theory Compendium, vol. 2",
 series       = "Oxford Logic Guides",
 volume       = "44",
 publisher    = "Oxford University Press",
)
@article(joyaltierney84,
 author       = "Andr{\'e} Joyal and Miles Tierney",
 year         = "1984",
 title        = "An extension of the Galois theory of Grothendieck",
 journal      = "Memoirs of the American Mathematical Society",
 volume       = "51",
 number       = "309",
 doi          = "10.1090/memo/0309",
)
@book(maclanemoerdijk92,
 author       = "Saunders {Mac Lane} and Ieke Moerdijk",
 year         = "1992",
 title        = "Sheaves in Geometry and Logic",
 publisher    = "Springer",
 doi          = "10.1007/978-1-4612-0927-0",
)
@article(Moer:CtsFibILT,
 author       = "I. Moerdijk",
 year         = "1986",
 title        = "Continuous Fibrations and Inverse Limits of Toposes",
 journal      = "Compositio Mathematica",
 volume       = "58",
 pages        = "45--72",
 url          = "http://www.numdam.org/item?id=CM_1986__58_1_45_0",
)
@phdthesis(nuiten,
 author       = "Joost Nuiten",
 year         = "2011",
 title        = "Bohrification of local nets of observables",
 school       = "Utrecht",
 url          = "http://arxiv.org/abs/1109.1397",
)
@article(PHLCC,
 author       = "Erik Palmgren and Steven Vickers",
 year         = "2007",
 title        = "Partial {H}orn Logic and Cartesian Categories",
 journal      = "Annals of Pure and Applied Logic",
 volume       = "145",
 number       = "3",
 pages        = "314--353",
 doi          = "10.1016/j.apal.2006.10.001",
)
@article(Spitters:SpaceMOSNCA,
 author       = "Bas Spitters",
 year         = "2012",
 title        = "{The Space of Measurement Outcomes as a Spectral Invariant for Non-Commutative Algebras}",
 journal      = "Foundations of Physics",
 volume       = "42",
 pages        = "896--908",
 doi          = "10.1007/s10701-011-9619-3",
)
@article(UniCharPP,
 author       = "S.J. Vickers and C.F. Townsend",
 year         = "2004",
 title        = "A Universal Characterization of the Double Powerlocale",
 journal      = "Theoretical Computer Science",
 volume       = "316",
 pages        = "297--321",
 doi          = "10.1016/j.tcs.2004.01.034",
)
@book(TVL,
 author       = "Steven Vickers",
 year         = "1989",
 title        = "Topology via Logic",
 publisher    = "Cambridge University Press",
)
@article(Infosys,
 author       = "Steven Vickers",
 year         = "1993",
 title        = "Information Systems for Continuous Posets",
 journal      = "Theoretical Computer Science",
 volume       = "114",
 pages        = "201--229",
 doi          = "10.1016/0304-3975(93)90072-2",
)
@article(PPExp,
 author       = "Steven Vickers",
 year         = "2004",
 title        = "The Double Powerlocale and Exponentiation: A Case Study in Geometric Reasoning",
 journal      = "Theory and Applications of Categories",
 volume       = "12",
 pages        = "372--422",
 url          = "http://www.tac.mta.ca/tac/index.html#vol12",
)
@article(EntSys,
 author       = "Steven Vickers",
 year         = "2004",
 title        = "Entailment Systems for Stably Locally Compact Locales",
 journal      = "Theoretical Computer Science",
 volume       = "316",
 pages        = "259--296",
 doi          = "10.1016/j.tcs.2004.01.033",
)
@article(LocCompA,
 author       = "Steven Vickers",
 year         = "2005",
 title        = "Localic Completion of Generalized Metric Spaces {I}",
 journal      = "Theory and Applications of Categories",
 volume       = "14",
 pages        = "328--356",
 url          = "http://www.tac.mta.ca/tac/index.html#vol14",
)
@article(CompLocFT,
 author       = "Steven Vickers",
 year         = "2006",
 title        = "Compactness in Locales and in Formal Topology",
 journal      = "Annals of Pure and Applied Logic",
 volume       = "137",
 pages        = "413--438",
 doi          = "10.1016/j.apal.2005.05.028",
)
@incollection(LocTopSp,
 author       = "Steven Vickers",
 year         = "2007",
 title        = "Locales and Toposes as Spaces",
 editor       = "Marco Aiello and Ian E. Pratt-Hartmann and Johan F.A.K. van Benthem",
 booktitle    = "Handbook of Spatial Logics",
 chapter      = "8",
 publisher    = "Springer",
 pages        = "429--496",
 doi          = "10.1007/978-1-4020-5587-4\_8",
)
@article(LocCompB,
 author       = "Steven Vickers",
 year         = "2009",
 title        = "Localic Completion of Generalized Metric Spaces {I}{I}: {P}owerlocales",
 journal      = "Journal of Logic and Analysis",
 volume       = "1",
 number       = "11",
 pages        = "1--48",
 doi          = "10.4115/jla.2009.1.11",
)
@unpublished(Vickers:Riesz,
 author       = "Steven Vickers",
 year         = "2011",
 title        = "A Monad of Valuation Locales",
 url          = "http://www.cs.bham.ac.uk/~sjv/Riesz.pdf",
)
@article(Vickers:ContIsGeom,
 author       = "Steven Vickers",
 year         = "2014",
 title        = "Continuity and Geometric Logic",
 journal      = "Journal of Applied Logic",
 volume       = "12",
 number       = "1",
 pages        = "14--27",
 doi          = "10.1016/j.jal.2013.07.004",
)
@phdthesis(ViglasThesis,
 author       = "K. Viglas",
 year         = "2004",
 title        = "Topos Aspects of the Extended {P}riestley Duality",
 school       = "Department of Computing, Imperial College, London",
)
@article(Wolters,
 author       = "Sander Wolters",
 year         = "2013",
 title        = "A Comparison of Two Topos-Theoretic Approaches to Quantum Theory.",
 journal      = "Communications in Mathematical Physics",
 volume       = "317",
 number       = "1",
 pages        = "3--53",
 doi          = "10.1007/s00220-012-1652-3",
 note         = "ArXiv:1010.2031",
)
@unpublished(Wolters/Halvorson,
 author       = "Sander A.M. Wolters and Hans Halvorson",
 year         = "2013",
 title        = "Independence Conditions for Nets of Local Algebras as Sheaf Conditions",
 url          = "http://arxiv.org/abs/1309.5639",
)