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@Misc{VV-IHP-talk,
author = {Voevodsky, Vladimir},
year = {2014},
title = {Univalent Foundations - new type-theoretic foundations of mathematics},
howpublished = {{s}lides from a talk at IHP, Paris, on April 22, 2014,
available at \url{https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2014_04_22_slides.pdf}}}
@Misc{VV-resizing,
author = {Voevodsky, Vladimir},
year = {2011},
title = {{Resizing Rules - their use and semantic justification}},
howpublished = {{s}lides from a talk available at \url{https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2011_Bergen.pdf}}}
@Misc{Swansea-Shulman,
author = {Shulman, Michael},
year = {2012},
title = {{Minicourse on Homotopy Type Theory}},
howpublished = {{slides from a talk, available} at \url{http://home.sandiego.edu/~shulman/hottminicourse2012/}}}
@Misc{Foundations,
AUTHOR = {Voevodsky, Vladimir},
title = {{Foundations: Development of the univalent foundations of mathematics in Coq}},
howpublished = {a Coq library of formalized proofs, available at \url{https://github.com/vladimirias/Foundations}}
}
@Misc{UniMath,
author = {Voevodsky, Vladimir and Ahrens, Benedikt and Grayson, Daniel and others},
title = {{UniMath --- a computer-checked library of univalent mathematics}},
howpublished = {{available} at \url{http://UniMath.org}}
}
@Misc{Lean,
title = {Lean theorem prover},
howpublished = {a proof assistant together with a library of formalized proofs, available at \url{https://github.com/leanprover/lean}}}
@Misc{RedPRL,
title = {{RedPRL}},
howpublished = {a proof assistant for Computational Cubical Type Theory together with a library of formalized proofs, available at \url{http://www.redprl.org/}}}
@Misc{HoTT,
title = {{The HoTT Library}},
howpublished = {a Coq library of formalized proofs, available at \url{https://github.com/HoTT/HoTT}}
}
@Misc{HoTT-Agda,
title = {{Homotopy Type Theory in Agda}},
howpublished = {an Agda library of formalized proofs, available at \url{https://github.com/HoTT/HoTT-Agda}}
}
@article {UniMath2015,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {An experimental library of formalized mathematics based on the
univalent foundations},
JOURNAL = {Math. Structures Comput. Sci.},
FJOURNAL = {Mathematical Structures in Computer Science. A Journal in the
Applications of Categorical, Algebraic and Geometric Methods
in Computer Science},
VOLUME = {25},
YEAR = {2015},
NUMBER = {5},
PAGES = {1278--1294},
ISSN = {0960-1295},
MRCLASS = {68N18 (03B35)},
MRNUMBER = {3340542},
DOI = {10.1017/S0960129514000577},
URL = {http://dx.doi.org/10.1017/S0960129514000577},
}
@inproceedings {MR0387023,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {Hauptsatz for the intuitionistic theory of iterated inductive
definitions},
BOOKTITLE = {Proceedings of the {S}econd {S}candinavian {L}ogic {S}ymposium
({U}niv. {O}slo, {O}slo, 1970)},
PAGES = {179--216. Studies in Logic and the Foundations of Mathematics,
Vol. 63},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1971},
MRCLASS = {02D99 (02C15)},
MRNUMBER = {0387023 (52 \#7870)},
MRREVIEWER = {Horst Luckhardt},
}
@incollection {MR0387009,
AUTHOR = {Martin-L{\"o}f, Per},
TITLE = {An intuitionistic theory of types: predicative part},
BOOKTITLE = {Logic {C}olloquium '73 ({B}ristol, 1973)},
PAGES = {73--118. Studies in Logic and the Foundations of Mathematics,
Vol. 80},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1975},
MRCLASS = {02C15 (02D99)},
MRNUMBER = {0387009 (52 \#7856)},
MRREVIEWER = {Horst Luckhardt},
}
@incollection {39,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Subsystems and regular quotients of {C}-systems},
BOOKTITLE = {A panorama of mathematics: pure and applied; Conference on Mathematics and its Applications, (Kuwait City, 2014)},
SERIES = {Contemp. Math.},
VOLUME = {658},
PAGES = {127--137},
PUBLISHER = {Amer. Math. Soc., Providence, RI},
YEAR = {2016},
MRCLASS = {03B15 (03B22 03F50 03G25)},
MRNUMBER = {3475277},
MRREVIEWER = {Krzysztof R. Kapulkin},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1090/conm/658/13124},
}
@Misc {mcall,
AUTHOR = {McAllester, David},
TITLE = {Morphoid Type Theory, A Typed Platonic Foundation for Mathematics},
note = {\arxiv{1407.7274}}
}
@Misc {42,
title = {C-system of a module over a monad on sets},
year = {2014},
author = {Voevodsky, Vladimir},
note = {\arxiv{1407.3394}}
}
@Misc {40,
title = {B-systems},
year = {2014},
note = {\arxiv{1410.5389}},
author = {Voevodsky, Vladimir}
}
@Misc {104,
title = {Products of families of types in the {C}-systems defined by a universe category},
year = {2015},
note = {\arxiv{1503.07072}},
author = {Voevodsky, Vladimir}
}
@Misc {103,
title = {Martin-{L}\"of identity types in the {C}-systems defined by a universe category},
year = {2015},
pages = {1--51},
note = {\arxiv{1505.06446}},
author = {Voevodsky, Vladimir}
}
@article {109,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {A {C}-system defined by a universe category},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {30},
YEAR = {2015},
number = {37},
PAGES = {1181--1215},
note = {\arxiv{1409.7925}},
ISSN = {1201-561X},
MRCLASS = {18Cxx (03G30)},
MRNUMBER = {3402489},
url = {http://www.tac.mta.ca/tac/volumes/30/37/30-37.pdf}
}
@article {110,
title = {Lawvere theories and {J}f-relative monads},
journal = {arXiv:1601.02158},
year = {2016},
pages = {1--21},
note = {\arxiv{1601.02158}},
author = {Voevodsky, Vladimir}
}
@article {112,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {Products of families of types and {$(\Pi,\lambda)$}-structures
on {C}-systems},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {31},
YEAR = {2016},
PAGES = {Paper No. 36, 1044--1094},
ISSN = {1201-561X},
MRCLASS = {03F50 (03B15 18C50 18D15)},
MRNUMBER = {3584698},
url = {http://www.tac.mta.ca/tac/volumes/31/36/31-36.pdf},
MRREVIEWER = {Thomas Streicher},
}
@article {MR3607210,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {The {$(\Pi, \lambda)$}-structures on the {C}-systems defined
by universe categories},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {32},
YEAR = {2017},
PAGES = {Paper No. 4, 113--121},
ISSN = {1201-561X},
MRCLASS = {18C50 (03B15 03F50 18D15)},
MRNUMBER = {3607210},
MRREVIEWER = {Thomas Streicher},
}
@article {MR3607209,
AUTHOR = {Voevodsky, Vladimir},
TITLE = {C-systems defined by universe categories: presheaves},
JOURNAL = {Theory Appl. Categ.},
FJOURNAL = {Theory and Applications of Categories},
VOLUME = {32},
YEAR = {2017},
PAGES = {Paper No. 3, 53--112},
ISSN = {1201-561X},
MRCLASS = {18D15 (03F50)},
MRNUMBER = {3607209},
}
@Misc{1211.2851,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu},
Title = {The {S}implicial {M}odel of {U}nivalent {F}oundations (after {V}oevodsky)},
Year = {2012},
note = {\arxiv{1211.2851}}
}
@Misc{1203.2553,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu and Voevodsky, Vladimir},
Title = {Univalence in Simplicial Sets},
Year = {2012},
note = {\arxiv{1203.2553}}
}
@Book{peano-principia,
author = {Peano, Giuseppe},
title = {Arithmetices principia: nova methodo},
publisher = {Fratres Bocca},
year = 1889,
url = {https://books.google.com/books?id=z80GAAAAYAAJ},
note = {See also \url{https://github.com/mdnahas/Peano_Book/} for a parallel translation by Vincent Verheyen}
}
@Book{hottbook,
author = {The {Univalent Foundations Program}},
title = {Homotopy Type Theory: Univalent Foundations of Mathematics},
publisher = {\url{https://homotopytypetheory.org/book}},
address = {Institute for Advanced Study},
year = 2013}
@Book{constructive-algebra,
author = {Mines, Ray and Richman, Fred and Ruitenburg Wim},
title = {A Course in Constructive Algebra},
publisher = {Springer-Verlag},
note = {Relevant Exercise 5 on page 133},
year = 1988}
@article {AwodeyBauer_prop_as_types,
AUTHOR = {Awodey, Steven and Bauer, Andrej},
TITLE = {Propositions as [types]},
JOURNAL = {J. Logic Comput.},
FJOURNAL = {Journal of Logic and Computation},
VOLUME = {14},
YEAR = {2004},
NUMBER = {4},
PAGES = {447--471},
ISSN = {0955-792X},
MRCLASS = {03B15 (03B20 03B45 18C50)},
MRNUMBER = {2081047},
DOI = {10.1093/logcom/14.4.447},
URL = {http://dx.doi.org/10.1093/logcom/14.4.447},
}
@incollection {MLTT79,
AUTHOR = {Martin-L\"of, Per},
TITLE = {Constructive mathematics and computer programming},
BOOKTITLE = {Logic, methodology and philosophy of science, {VI}
({H}annover, 1979)},
SERIES = {Stud. Logic Found. Math.},
VOLUME = {104},
PAGES = {153--175},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {1982},
MRCLASS = {03F50 (03B70 03F55 68Q45)},
MRNUMBER = {682410},
MRREVIEWER = {B. H. Mayoh},
DOI = {10.1016/S0049-237X(09)70189-2},
URL = {http://dx.doi.org/10.1016/S0049-237X(09)70189-2},
}
@incollection {MR1678360,
AUTHOR = {Makkai, M.},
TITLE = {Towards a categorical foundation of mathematics},
BOOKTITLE = {Logic {C}olloquium '95 ({H}aifa)},
SERIES = {Lecture Notes Logic},
VOLUME = {11},
PAGES = {153--190},
PUBLISHER = {Springer, Berlin},
YEAR = {1998},
MRCLASS = {03B15 (00A30 03A05 03G30 18A15 18D05)},
MRNUMBER = {1678360},
MRREVIEWER = {Peter Johnstone},
DOI = {10.1007/978-3-662-22108-2_11},
URL = {http://dx.doi.org/10.1007/978-3-662-22108-2_11},
}
@article {MR2463991,
AUTHOR = {Gonthier, Georges},
TITLE = {Formal proof---the four-color theorem},
JOURNAL = {Notices Amer. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical Society},
VOLUME = {55},
YEAR = {2008},
NUMBER = {11},
PAGES = {1382--1393},
ISSN = {0002-9920},
MRCLASS = {05C15 (68T15)},
MRNUMBER = {2463991},
MRREVIEWER = {Solomon Marcus},
}
@article {MR1506041,
AUTHOR = {Russell, Bertrand},
TITLE = {Mathematical {L}ogic as {B}ased on the {T}heory of {T}ypes},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {30},
YEAR = {1908},
NUMBER = {3},
PAGES = {222--262},
ISSN = {0002-9327},
MRCLASS = {DML},
MRNUMBER = {1506041},
DOI = {10.2307/2369948},
URL = {http://dx.doi.org/10.2307/2369948},
}
@article {bernays-7,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {VII}},
JOURNAL = {J. Symb. Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {19},
YEAR = {1954},
PAGES = {81--96},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0066320},
MRREVIEWER = {O. Frink},
}
@article {bernays-6,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {VI}},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {13},
YEAR = {1948},
PAGES = {65--79},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0025421},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2267328},
URL = {http://dx.doi.org/10.2307/2267328},
}
@article {bernays-5,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {V}. {G}eneral set theory},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {8},
YEAR = {1943},
PAGES = {89--106},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0009761},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2271051},
URL = {http://dx.doi.org/10.2307/2271051},
}
@article {bernays-4,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {7},
YEAR = {1942},
PAGES = {133--145},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0007731},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2268110},
URL = {http://dx.doi.org/10.2307/2268110},
}
@article {bernays-3,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {III}. {I}nfinity and
enumerability. {A}nalysis},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {7},
YEAR = {1942},
PAGES = {65--89},
ISSN = {0022-4812},
MRCLASS = {02.0X},
MRNUMBER = {0006333},
MRREVIEWER = {O. Frink},
DOI = {10.2307/2266303},
URL = {http://dx.doi.org/10.2307/2266303},
}
@article {bernays-2,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {P}art {II}},
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MRNUMBER = {0003382},
MRREVIEWER = {H. B. Curry},
DOI = {10.2307/2267281},
URL = {http://dx.doi.org/10.2307/2267281},
}
@article {bernays-1,
AUTHOR = {Bernays, Paul},
TITLE = {A system of axiomatic set theory. {P}art {I}},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {2},
YEAR = {1937},
PAGES = {65--77},
DOI = {10.2307/2268862},
http = {URL://dx.doi.org/10.2307/2268862},
}
@Misc{Coq,
author = {The Coq Development Team},
title = {The Coq Proof Assistant},
howpublished = {Available at \url{https://coq.inria.fr/}}
}
@Misc{1610.04591,
Author = {Bauer, Andrej and Gross, Jason and Lumsdaine, Peter LeFanu and Shulman, Mike and Sozeau, Matthieu and Spitters, Bas},
Title = {{The HoTT Library: A formalization of homotopy type theory in Coq}},
Year = {2016},
note = {\arxiv{1610.04591}},
}
@article {IMGelfand,
AUTHOR = {Beilinson, A.},
TITLE = {I. {M}. {G}elfand and his seminar---a presence},
JOURNAL = {Notices Amer. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical Society},
VOLUME = {63},
YEAR = {2016},
NUMBER = {3},
PAGES = {295--298},
ISSN = {0002-9920},
note = {\arxiv{1505.00710}},
MRCLASS = {01A70},
MRNUMBER = {3445168},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1090/noti1337},
}
@Misc{1605.03227,
Author = {Hou, Kuen-Bang Hou (Favonia) and Finster, Eric and Licata, Dan and Lumsdaine, Peter LeFanu},
Title = {{A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory}},
Year = {2016},
note = {\arxiv{1605.03227}},
}
@Misc{RezkBM,
Author = {Rezk, Charles},
Title = {{Proof of the Blakers-Massey Theorem}},
note = {Available at \url{https://faculty.math.illinois.edu/~rezk/freudenthal-and-blakers-massey.pdf}},
}
@Misc{1703.09050,
Author = {Anel, Mathieu and Biedermann, Georg and Finster, Eric and Joyal, Andr\'e},
Title = {{A Generalized Blakers-Massey Theorem}},
Year = {2017},
note = {\arxiv{1703.09050}},
}
@Misc{1703.09632,
Author = {Anel, Mathieu and Biedermann, Georg and Finster, Eric and Joyal, Andr\'e},
Title = {{Goodwillie's Calculus of Functors and Higher Topos Theory}},
Year = {2017},
note = {\arxiv{1703.09632}},
}
@Misc{1709.09519,
Author = {Kapulkin, Chris and Szumiło, Karol},
Title = {{Internal Language of Finitely Complete $(\infty,1)$-categories}},
Year = {2017},
note = {\arxiv{1709.09519}},
}
@Misc{1610.00037,
Author = {Kapulkin, Chris and Lumsdaine, Peter LeFanu},
Title = {{The homotopy theory of type theories}},
Year = {2016},
note = {\arxiv{1610.00037}},
}
@Misc{1606.05916,
Author = {Brunerie, Guillaume},
Title = {{On the homotopy groups of spheres in homotopy type theory}},
Year = {2016},
note = {{Ph.D.} thesis, \arxiv{1606.05916}},
}
@Misc{1710.10307,
Author = {Brunerie, Guillaume},
Title = {{The James construction and $\pi_4(\mathbb{S}^3)$ in homotopy type theory}},
Year = {2017},
note = {\arxiv{1710.10307}, accepted for publication in the Journal of Automated Reasoning},
}
@Misc{cubicaltt,
author = {Cohen, Cyril and Coquand, Thierry and Huber, Simon and M\"ortberg, Anders},
howpublished = {the proof assistant {\tt cubical}, written in Haskell, available at \url{https://github.com/mortberg/cubicaltt}},
title = {Experimental implementation of Cubical Type Theory}
}
@article{1611.02108,
author = {Cohen, Cyril and Coquand, Thierry and Huber, Simon and M\"ortberg, Anders},
title = {{Cubical Type Theory: a constructive interpretation of the univalence axiom}},
note = {To appear in the post-proceedings of TYPES 2015. Preprint avaiable at https://arxiv.org/abs/1611.02108},
year = 2015,
}
@Misc{1705.07088,
Author = {Lumsdaine, Peter LeFanu and Shulman, Mike},
Title = {{Semantics of higher inductive types}},
Year = {2017},
note = {\arxiv{1705.07088}},
}
@Misc{1703.03007,
Author = {Shulman, Michael},
Title = {{Homotopy type theory: the logic of space}},
Year = {2017},
note = {\arxiv{1703.03007}},
}
@article {0709.0248,
AUTHOR = {Awodey, Steve and Warren, Michael A.},
TITLE = {Homotopy theoretic models of identity types},
JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
Society},
VOLUME = {146},
YEAR = {2009},
NUMBER = {1},
PAGES = {45--55},
ISSN = {0305-0041},
MRCLASS = {03B15 (03B35 18G99 55U35)},
MRNUMBER = {2461866},
note = {\arxiv{0709.0248}},
MRREVIEWER = {Richard F. Blute},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1017/S0305004108001783},
}
@Misc{1509.07584,
Author = {Michael Shulman},
Title = {{Brouwer's fixed-point theorem in real-cohesive homotopy type theory}},
Year = {2015},
note = {\arxiv{1509.07584}},
}
@incollection {MR0274219,
AUTHOR = {de Bruijn, N. G.},
TITLE = {The mathematical language {AUTOMATH}, its usage, and some of
its extensions},
BOOKTITLE = {Symposium on {A}utomatic {D}emonstration ({V}ersailles, 1968)},
PAGES = {29--61},
PUBLISHER = {Lecture Notes in Mathematics, Vol. 125. Springer, Berlin},
YEAR = {1970},
MRCLASS = {94.40},
MRNUMBER = {0274219},
MRREVIEWER = {T. Rus},
}
@article {MR3363596,
AUTHOR = {Coquand, Thierry},
TITLE = {Th\'eorie des types d\'ependants et axiome d'univalence},
JOURNAL = {Ast\'erisque},
FJOURNAL = {Ast\'erisque},
NUMBER = {367-368},
YEAR = {2015},
PAGES = {Exp. No. 1085, x, 367--386},
ISSN = {0303-1179},
ISBN = {978-2-85629-804-6},
MRCLASS = {03B15 (18B40 55U40)},
MRNUMBER = {3363596},
MRREVIEWER = {Luca Paolini},
}
@incollection {MR3566711,
AUTHOR = {Hou, Kuen-Bang and Shulman, Michael},
TITLE = {The {S}eifert--van {K}ampen theorem in homotopy type theory},
BOOKTITLE = {Computer science logic 2016},
SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
VOLUME = {62},
PAGES = {Art. No. 22, 16},
PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
YEAR = {2016},
MRCLASS = {55U35 (03B40 18G30 68N18)},
MRNUMBER = {3566711},
}
@article {MR3340533,
AUTHOR = {Ahrens, Benedikt and Kapulkin, Krzysztof and Shulman, Michael},
TITLE = {Univalent categories and the {R}ezk completion},
JOURNAL = {Math. Structures Comput. Sci.},
FJOURNAL = {Mathematical Structures in Computer Science. A Journal in the
Applications of Categorical, Algebraic and Geometric Methods
in Computer Science},
VOLUME = {25},
YEAR = {2015},
NUMBER = {5},
PAGES = {1010--1039},
ISSN = {0960-1295},
MRCLASS = {18B99 (03B15)},
MRNUMBER = {3340533},
MRREVIEWER = {Thomas Streicher},
URL = {https://doi-org.proxy2.library.illinois.edu/10.1017/S0960129514000486},
}
@incollection {MR3323808,
AUTHOR = {Licata, Daniel R. and Shulman, Michael},
TITLE = {Calculating the fundamental group of the circle in homotopy
type theory},
BOOKTITLE = {2013 28th {A}nnual {ACM}/{IEEE} {S}ymposium on {L}ogic in
{C}omputer {S}cience ({LICS} 2013)},
PAGES = {223--232},
PUBLISHER = {IEEE Computer Soc., Los Alamitos, CA},
YEAR = {2013},
MRCLASS = {03B15 (55U40)},
MRNUMBER = {3323808},
MRREVIEWER = {Thomas John Hunter},
}
@incollection {MR3281415,
AUTHOR = {Bezem, Marc and Coquand, Thierry and Huber, Simon},
TITLE = {A model of type theory in cubical sets},
BOOKTITLE = {19th {I}nternational {C}onference on {T}ypes for {P}roofs and
{P}rograms},
SERIES = {LIPIcs. Leibniz Int. Proc. Inform.},
VOLUME = {26},
PAGES = {107--128},
PUBLISHER = {Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern},
YEAR = {2014},
MRCLASS = {03B15},
MRNUMBER = {3281415},
}
@Article{ Tsem1,
author = "Tsementzis, D.",
title = "Univalent foundations as structuralist foundations",
journal = "Synthese",
year = "2017",
month = "Sep",
day = "01",
volume = "194",
number = "9",
pages = "3583--3617",
doi = "10.1007/s11229-016-1109-x"
}
@article{Tsem2,
author = {Tsementzis, D.},
title = {What is a Higher-Level Set?†},
journal = {Philosophia Mathematica},
note= {(forthcoming), {Available at \url{https://academic.oup.com/philmat/article-abstract/2895117/What-is-a-Higher-Level-Set}}},
volume = {},
number = {},
pages = {},
year = {2017},
doi = {10.1093/philmat/nkw032},
URL = { + http://dx.doi.org/10.1093/philmat/nkw032},
eprint = {/oup/backfile/content_public/journal/philmat/pap/10.1093_philmat_nkw032/2/nkw032.pdf},
}
@article{Tsem3,
title={Foundations and Philosophy},
author={Tsementzis, D. and Halvorson, H.},
journal={Philosopher's Imprint (forthcoming)},
note={Available at \url{http://philsci-archive.pitt.edu/13504/}},
year={2017}
}
@article{Tsem4,
title={A Meaning Explanation for HoTT},
author={Tsementzis, D.},
note={Available at \url{http://philsci-archive.pitt.edu/12824/}},
year={2016}
}
@Misc {harper-et-al-1,
AUTHOR = {Angiuli, Carlo and Harper, Robert and Wilson, Todd},
TITLE = {{Computational higher type theory I: Abstract cubical realizability}},
year = {2016},
note = {\arxiv{1604.08873}}
}
@Misc {harper-et-al-2,
AUTHOR = {Angiuli, Carlo and Harper, Robert},
TITLE = {{Computational higher type theory II: Dependent cubical realizability}},
year = {2016},
note = {\arxiv{1606.09638}}
}
@Misc {harper-et-al-3,
AUTHOR = {Angiuli, Carlo and Hou, Kuen-Bang and Harper, Robert},
TITLE = {{Computational Higher Type Theory III: Univalent Universes and Exact Equality}},
year = {2017},
note = {\arxiv{1712.01800}}
}
@Misc {harper-et-al-4,
AUTHOR = {Cavallo, Evan and Harper, Robert},
TITLE = {{Computational Higher Type Theory IV: Inductive Types}},
year = {2018},
note = {\arxiv{1801.01568}}
}
@Misc {cart-cube,
author = {Angiuli, Carlo and Brunerie, Guillaume and Coquand, Thierry and Hou, Kuen-Bang and Harper, Robert and Licata, Daniel R.},
title = {{Cartesian Cubical Type Theory}},
year = {2017},
note = {{a}vailable at \url{https://github.com/dlicata335/cart-cube/raw/master/cart-cube.pdf}}}
@article{10.2307/986491,
ISSN = {0003049X},
URL = {http://www.jstor.org/stable/986491},
author = {Kenneth I. Appel},
journal = {Proceedings of the American Philosophical Society},
number = {1},
pages = {35-39},
publisher = {American Philosophical Society},
title = {The Use of the Computer in the Proof of the Four Color Theorem},
volume = {128},
year = {1984}
}
@article {MR0543793,
AUTHOR = {Appel, K. and Haken, W. and Koch, J.},
TITLE = {Every planar map is four colorable. {II}. {R}educibility},
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FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {21},
YEAR = {1977},
NUMBER = {3},
PAGES = {491--567},
ISSN = {0019-2082},
MRCLASS = {05C15},
MRNUMBER = {0543793},
MRREVIEWER = {Frank Allaire},
URL = {http://projecteuclid.org/euclid.ijm/1256049012},
}
@article {MR0543792,
AUTHOR = {Appel, K. and Haken, W.},
TITLE = {Every planar map is four colorable. {I}. {D}ischarging},
JOURNAL = {Illinois J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {21},
YEAR = {1977},
NUMBER = {3},
PAGES = {429--490},
ISSN = {0019-2082},
MRCLASS = {05C15},
MRNUMBER = {0543792},
MRREVIEWER = {Frank Allaire},
URL = {http://projecteuclid.org/euclid.ijm/1256049011},
}
@InProceedings{10.1007/978-3-642-39634-2_14,
author="Gonthier, Georges
and Asperti, Andrea
and Avigad, Jeremy
and Bertot, Yves
and Cohen, Cyril
and Garillot, Fran{\c{c}}ois
and Le Roux, St{\'e}phane
and Mahboubi, Assia
and O'Connor, Russell
and Ould Biha, Sidi
and Pasca, Ioana
and Rideau, Laurence
and Solovyev, Alexey
and Tassi, Enrico
and Th{\'e}ry, Laurent",
editor="Blazy, Sandrine
and Paulin-Mohring, Christine
and Pichardie, David",
title="A Machine-Checked Proof of the Odd Order Theorem",
booktitle="Interactive Theorem Proving",
year="2013",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="163--179",
abstract="This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries of formalized mathematics, including results in finite group theory, linear algebra, Galois theory, and the theories of the real and complex algebraic numbers.",
isbn="978-3-642-39634-2"
}
@article{kepler,
title={{A formal proof of the Kepler conjecture}},
volume={5}, DOI={10.1017/fmp.2017.1}, journal={Forum of Mathematics, Pi}, publisher={Cambridge University Press},
author={Hales, Thomas and Adams, Mark and Bauer, Gertrud and Dang, Dat Tat and Harrison, John and Hoang, Truong Le and Kaliszyk, Cezary and Magron, Victor and Mclaughlin, Sean and Nguyen, Thang Tat and others},
year={2017},
pages={e2}
}
@InProceedings{CPP16p122,
author = {van Doorn, Floris},
title = {{Constructing the Propositional Truncation using Non-recursive HITs}},
booktitle = {Proc.\ Certified Proofs and Programs (CPP), 2016},
publisher = {ACM},
pages = {122--129},
doi = {10.1145/2854065.2854076},
year = {2016},
note = {\arxiv{1512.02274}}
}
@Misc{1802.01170,
title = {{On Higher Inductive Types in Cubical Type Theory}},
author = {Thierry, Coquand and Huber, Simon and M\"ortberg, Anders},
year = {2018},
note = {\arxiv{1802.01170}}}
@Misc{1802.02191,
title = {{Cellular Cohomology in Homotopy Type Theory}},
author = {Buchholtz, Ulrik and Hou, Kuen-Bang (Favonia)},
year = {February, 2018},
note = {\arxiv{1802.02191}}}
@article{Kleiner-group-survey,
AUTHOR = {Kleiner, Israel},
TITLE = {The evolution of group theory: a brief survey},
JOURNAL = {Math. Mag.},
FJOURNAL = {Mathematics Magazine},
VOLUME = {59},
YEAR = {1986},
NUMBER = {4},
PAGES = {195--215},
DOI = {10.2307/2690312}
}
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AUTHOR = {Hawkins, Thomas},
TITLE = {The {\it {E}rlanger {P}rogramm} of {F}elix {K}lein:
reflections on its place in the history of mathematics},
JOURNAL = {Historia Math.},
FJOURNAL = {Historia Mathematica},
VOLUME = {11},
YEAR = {1984},
NUMBER = {4},
PAGES = {442--470},
DOI = {10.1016/0315-0860(84)90028-4}
}
@article {Klein-EP-en,
AUTHOR = {Klein, Felix},
TITLE = {A comparative review of recent researches in geometry},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical Society},
VOLUME = {2},
YEAR = {1893},
NUMBER = {10},
PAGES = {215--249},
DOI = {10.1090/S0002-9904-1893-00147-X}
}
@article {Klein-EP-de,
AUTHOR = {Klein, Felix},
TITLE = {Vergleichende {B}etrachtungen \"{u}ber neuere geometrische
{F}orschungen},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {43},
YEAR = {1893},
NUMBER = {1},
PAGES = {63--100},
DOI = {10.1007/BF01446615}
}
@book{Wussing-genesis,
AUTHOR = {Wussing, Hans},
TITLE = {The genesis of the abstract group concept},
NOTE = {A contribution to the history of the origin of abstract group
theory,
Translated from the German by Abe Shenitzer and Hardy Grant},
PUBLISHER = {MIT Press, Cambridge, MA},
YEAR = {1984},
PAGES = {331}
}
@article{Le-premises,
AUTHOR = {L\^{e}, Fran\c{c}ois},
TITLE = {``{G}eometrical equations'': forgotten premises of {F}elix
{K}lein's {\it {E}rlanger {P}rogramm}},
JOURNAL = {Historia Math.},
FJOURNAL = {Historia Mathematica},
VOLUME = {42},
YEAR = {2015},
NUMBER = {3},
PAGES = {315--342},
DOI = {10.1016/j.hm.2014.11.002}
}
@Misc{circlerec-Dan,
author = {Grayson, Dan},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/master/UniMath/SyntheticHomotopyTheory/Circle.v}},
title = {The file containing the proof of circle recursion}
}
@Misc{circleind-Dan,
author = {Grayson, Dan},
title = {The file containing the proof of circle induction},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/master/UniMath/SyntheticHomotopyTheory/Circle2.v}},
}
@Misc{circleind-Dan-theorem,
author = {Grayson, Dan},
title = {The statement and proof of the circle induction theorem, a snapshot},
howpublished = {\url{https://github.com/UniMath/UniMath/blob/d5e570ba972bca92ec6b9023e5166034b0d79654/UniMath/SyntheticHomotopyTheory/Circle2.v\#L268}},
}
@Misc{circleind-Mike,
author = {Shulman, Mike},
howpublished = {\url{https://groups.google.com/d/msg/homotopytypetheory/hE1eY-v_Kes/bdSoAxC9224J}},
title = {Proof sketch of circle induction}
}
@Misc{ Rijke-Join,
title = {The join construction},
author = {Egbert Rijke},
year = {2017},
eprint = {1701.07538},
archiveprefix = {arXiv}
}
@Book{ Toth-FMG,
author = {Toth, Gabor},
title = {Finite {M}\"{o}bius groups, minimal immersions of spheres,
and moduli},
series = {Universitext},
publisher = {Springer-Verlag, New York},
year = {2002},
pages = {xvi+317},
isbn = {0-387-95323-X},
doi = {10.1007/978-1-4613-0061-8}
}
@Book{ Klein-Ikosaeder,
author = {Klein, Felix},
title = {Vorlesungen \"{u}ber das {I}kosaeder und die
{A}ufl\"{o}sung der {G}leichungen vom f\"{u}nften {G}rade},
note = {Reprint of the 1884 original, Edited, with an introduction
and commentary by Peter Slodowy},
publisher = {Birkh\"{a}user Verlag, Basel; B. G. Teubner, Stuttgart},
year = {1993},
pages = {xxviii+viii+343},
isbn = {3-7643-2454-6},
doi = {10.1007/978-3-0348-8594-2}
}
@Book{ Klein-Icosahedron,
author = {Klein, Felix},
title = {Lectures on the icosahedron and the solution of equations
of the fifth degree},
edition = {revised},
note = {Translated into English by George Gavin Morrice},
publisher = {Dover Publications, Inc., New York, N.Y.},
year = {1956},
pages = {xvi+289}
}
@Book{ Carter-VGT,