# To normalize:
# bibtool --preserve.key.case=on --preserve.keys=on --pass.comments=on --print.use.tab=off -s -i docs/references.bib -o docs/references.bib
# https://www.zbmath.org/ and https://mathscinet.ams.org/mathscinet
# (or the free tool https://mathscinet.ams.org/mrlookup)
# are good sources of complete bibtex entries for mathematics
# To link to an entry in `references.bib`, use the following formats:
# [Author, *Title* (optional location)][bibkey]
@Article{ ahrens2017,
author = {Benedikt Ahrens and Peter LeFanu Lumsdaine},
year = {2019},
title = {Displayed Categories},
journal = {Logical Methods in Computer Science},
volume = {15},
issue = {1},
doi = {10.23638/LMCS-15(1:20)2019}
}
@Book{ aluffi2016,
title = {Algebra: Chapter 0},
author = {Aluffi, Paolo},
series = {Graduate Studies in Mathematics},
volume = {104},
year = {2016},
publisher = {American Mathematical Society},
edition = {Reprinted with corrections by the American Mathematical
Society}
}
@Book{ atiyah-macdonald,
author = {Atiyah, M. F. and Macdonald, I. G.},
title = {Introduction to commutative algebra},
publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
Mills, Ont.},
year = {1969},
pages = {ix+128},
mrclass = {13.00},
mrnumber = {0242802},
mrreviewer = {J. A. Johnson}
}
@InProceedings{ avigad-carneiro-hudon2019,
author = {Jeremy Avigad and Mario M. Carneiro and Simon Hudon},
editor = {John Harrison and John O'Leary and Andrew Tolmach},
title = {Data Types as Quotients of Polynomial Functors},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
series = {LIPIcs},
volume = {141},
pages = {6:1--6:19},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.6},
doi = {10.4230/LIPIcs.ITP.2019.6},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/AvigadCH19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Misc{ avigad_moura_kong-2017,
author = {Jeremy Avigad and Leonardo de Moura and Soonho Kong},
title = {{T}heorem {P}roving in {L}ean},
year = {2017},
howpublished = {\url{https://leanprover.github.io/theorem_proving_in_lean/}}
}
@Book{ axler2015,
author = {Sheldon Axler},
title = {Linear algebra done right. 3rd ed.},
fjournal = {Undergraduate Texts in Mathematics},
journal = {Undergraduate Texts Math.},
issn = {0172-6056; 2197-5604/e},
edition = {3rd ed.},
isbn = {978-3-319-11079-0/hbk; 978-3-319-11080-6/ebook},
pages = {xvii + 340},
year = {2015},
publisher = {Springer}
}
@Book{ beals2004,
author = {Richard Beals},
title = {Analysis. An introduction},
publisher = {Cambridge University Press},
isbn = {0521600472},
year = {2004}
}
@Article{ bernstein1912,
author = {Bernstein, S.},
year = {1912},
title = {Démonstration du théorème de Weierstrass fondée sur le
calcul des probabilités},
journal = {Comm. Kharkov Math. Soc.},
volume = {13},
number = {1–2}
}
@InProceedings{ beylin1996,
author = "Beylin, Ilya and Dybjer, Peter",
editor = "Berardi, Stefano and Coppo, Mario",
title = "Extracting a proof of coherence for monoidal categories
from a proof of normalization for monoids",
booktitle = "Types for Proofs and Programs",
year = "1996",
publisher = "Springer Berlin Heidelberg",
address = "Berlin, Heidelberg",
pages = "47--61",
abstract = "This paper studies the problem of coherence in category
theory from a type-theoretic viewpoint. We first show how a
Curry-Howard interpretation of a formal proof of
normalization for monoids almost directly yields a
coherence proof for monoidal categories. Then we formalize
this coherence proof in intensional intuitionistic type
theory and show how it relies on explicit reasoning about
proof objects for intensional equality. This formalization
has been checked in the proof assistant ALF.",
isbn = "978-3-540-70722-6"
}
@Book{ borceux-vol1,
title = {Handbook of Categorical Algebra: Volume 1, Basic Category
Theory},
author = {Borceux, Francis},
series = {Encyclopedia of Mathematics},
volume = {50},
year = {1994},
publisher = {Cambridge University Press}
}
@Book{ borceux-vol2,
title = {Handbook of Categorical Algebra: Volume 2, Categories and
Structures},
author = {Borceux, Francis},
series = {Encyclopedia of Mathematics},
volume = {51},
year = {1994},
publisher = {Cambridge University Press}
}
@Book{ bourbaki1966,
author = {Bourbaki, Nicolas},
title = {Elements of mathematics. {G}eneral topology. {P}art 1},
publisher = {Hermann, Paris; Addison-Wesley Publishing Co., Reading,
Mass.-London-Don Mills, Ont.},
year = {1966},
pages = {vii+437},
mrclass = {54.00 (00.00)},
mrnumber = {0205210}
}
@Book{ bourbaki1975,
author = {Bourbaki, Nicolas},
title = {Lie groups and {L}ie algebras. {C}hapters 1--3},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the French, Reprint of the 1989 English
translation},
publisher = {Springer-Verlag, Berlin},
year = {1998},
pages = {xviii+450},
isbn = {3-540-64242-0},
mrclass = {17Bxx (00A05 22Exx)},
mrnumber = {1728312}
}
@Book{ bourbaki1975b,
author = {Bourbaki, Nicolas},
title = {Lie groups and {L}ie algebras. {C}hapters 7--9},
series = {Elements of Mathematics (Berlin)},
note = {Translated from the 1975 and 1982 French originals by Andrew
Pressley},
publisher = {Springer-Verlag, Berlin},
year = {2005},
pages = {xii+434},
isbn = {3-540-43405-4},
mrclass = {17-01 (01A75 22-01)},
mrnumber = {2109105}
}
@Book{ calugareanu,
author = {C\v{a}lug\v{a}reanu, Grigore},
year = {2000},
month = {01},
pages = {},
title = {Lattice Concepts of Module Theory},
doi = {10.1007/978-94-015-9588-9}
}
@Misc{ carneiro2018matiyasevic,
title = {A {L}ean formalization of {M}atiyasevi{\v c}'s theorem},
author = {Mario Carneiro},
year = {2018},
eprint = {1802.01795},
archiveprefix = {arXiv},
primaryclass = {math.LO}
}
@InProceedings{ carneiro2019,
author = {Mario M. Carneiro},
editor = {John Harrison and John O'Leary and Andrew Tolmach},
title = {Formalizing Computability Theory via Partial Recursive
Functions},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
series = {LIPIcs},
volume = {141},
pages = {12:1--12:17},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.12},
doi = {10.4230/LIPIcs.ITP.2019.12},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/Carneiro19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Book{ cassels1967algebraic,
title = {Algebraic number theory: proceedings of an instructional
conference},
author = {Cassels, John William Scott and Fr{\"o}lich, Albrecht},
year = {1967},
publisher = {Academic Pr}
}
@InProceedings{ CL21,
author = {Commelin, Johan and Lewis, Robert Y.},
title = {Formalizing the Ring of Witt Vectors},
year = {2021},
isbn = {9781450382991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3437992.3439919},
doi = {10.1145/3437992.3439919},
abstract = {The ring of Witt vectors W R over a base ring R is an
important tool in algebraic number theory and lies at the
foundations of modern p-adic Hodge theory. W R has the
interesting property that it constructs a ring of
characteristic 0 out of a ring of characteristic p > 1,
and it can be used more specifically to construct from a
finite field containing ℤ/pℤ the corresponding
unramified field extension of the p-adic numbers ℚp
(which is unique up to isomorphism). We formalize the
notion of a Witt vector in the Lean proof assistant, along
with the corresponding ring operations and other algebraic
structure. We prove in Lean that, for prime p, the ring of
Witt vectors over ℤ/pℤ is isomorphic to the ring of
p-adic integers ℤp. In the process we develop idioms to
cleanly handle calculations of identities between
operations on the ring of Witt vectors. These calculations
are intractable with a naive approach, and require a proof
technique that is usually skimmed over in the informal
literature. Our proofs resemble the informal arguments
while being fully rigorous.},
booktitle = {Proceedings of the 10th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
pages = {264–277},
numpages = {14},
keywords = {ring theory, formal math, proof assistant, Lean, number
theory},
location = {Virtual, Denmark},
series = {CPP 2021}
}
@Book{ conway2001,
author = {Conway, J. H.},
title = {On numbers and games},
edition = {Second},
publisher = {A K Peters, Ltd., Natick, MA},
year = {2001},
pages = {xii+242},
isbn = {1-56881-127-6},
mrclass = {00A08 (05-01 91A05)},
mrnumber = {1803095}
}
@Article{ dyckhoff_1992,
author = {Dyckhoff, Roy},
title = {Contraction-free sequent calculi for intuitionistic
logic},
journal = {Journal of Symbolic Logic},
number = {3},
year = {1992},
pages = {795–807},
volume = {57},
publisher = {Cambridge University Press},
doi = {10.2307/2275431}
}
@Book{ EinsiedlerWard2017,
author = {Einsiedler, Manfred and Ward, Thomas},
title = {Functional Analysis, Spectral Theory, and Applications},
year = 2017,
publisher = {Springer},
doi = {10.1007/978-3-319-58540-6}
}
@Book{ Elephant,
title = {Sketches of an Elephant – A Topos Theory Compendium},
author = {Peter Johnstone},
year = {2002},
publisher = {Oxford University Press}
}
@Article{ erdosrenyisos,
author = {P. Erd\"os, A.R\'enyi, and V. S\'os},
title = {On a problem of graph theory},
journal = {Studia Sci. Math.},
number = {1},
year = {1966},
pages = {215--235},
url = {https://www.renyi.hu/~p_erdos/1966-06.pdf}
}
@Book{ Federer1996,
author = {Herbert Federer},
title = {Geometric Measure Theory},
series = {Classics in Mathematics},
year = {1996},
publisher = {Springer-Verlag Berlin Heidelberg},
issn = {1431-0821},
doi = {10.1007/978-3-642-62010-2},
numpages = {677}
}
@Article{ FennRourke1992,
author = {Fenn, Roger and Rourke, Colin},
journal = {Journal of Knot Theory and its Ramifications},
title = {Racks and links in codimension two},
year = {1992},
issn = {0218-2165},
number = {4},
pages = {343--406},
volume = {1},
doi = {10.1142/S0218216592000203},
keywords = {57M25 (57N10)},
mrnumber = {1194995}
}
@InProceedings{ fuerer-lochbihler-schneider-traytel2020,
author = {Basil F{\"{u}}rer and Andreas Lochbihler and Joshua
Schneider and Dmitriy Traytel},
editor = {Nicolas Peltier and Viorica Sofronie{-}Stokkermans},
title = {Quotients of Bounded Natural Functors},
booktitle = {Automated Reasoning - 10th International Joint Conference,
{IJCAR} 2020, Paris, France, July 1-4, 2020, Proceedings,
Part {II}},
series = {Lecture Notes in Computer Science},
volume = {12167},
pages = {58--78},
publisher = {Springer},
year = {2020},
url = {https://doi.org/10.1007/978-3-030-51054-1\_4},
doi = {10.1007/978-3-030-51054-1\_4},
timestamp = {Mon, 06 Jul 2020 09:05:32 +0200},
biburl = {https://dblp.org/rec/conf/cade/FurerLST20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@InProceedings{ Gallier2011Notes,
title = {Notes on Differential Geometry and Lie Groups},
author = {J. Gallier and J. Quaintance},
year = {2011},
url = {https://www.cis.upenn.edu/~cis610/diffgeom-n.pdf}
}
@Article{ ghys87:groupes,
author = {Étienne Ghys},
title = {Groupes d'homeomorphismes du cercle et cohomologie
bornee},
journal = {Contemporary Mathematics},
year = 1987,
volume = 58,
number = {III},
pages = {81-106},
doi = {10.1090/conm/058.3/893858},
language = {french}
}
@Book{ gouvea1997,
author = {Gouv\^{e}a, Fernando Q.},
title = {{$p$}-adic numbers},
series = {Universitext},
edition = {Second},
note = {An introduction},
publisher = {Springer-Verlag, Berlin},
year = {1997},
pages = {vi+298},
isbn = {3-540-62911-4},
mrclass = {11S80 (11-01 12J25)},
mrnumber = {1488696},
doi = {10.1007/978-3-642-59058-0},
url = {https://doi.org/10.1007/978-3-642-59058-0}
}
@Book{ Gratzer2011,
author = {Gr{\"a}tzer, George},
title = {Lattice Theory: Foundation},
year = {2011},
publisher = {Springer, Basel},
pages = {xxx+614},
isbn = {978-3-0348-0018-1},
doi = {10.1007/978-3-0348-0018-1},
mrnumber = {2768581}
}
@Article{ Gusakov2021,
author = {Alena Gusakov and Bhavik Mehta and Kyle A. Miller},
title = {Formalizing Hall's Marriage Theorem in Lean},
eprint = {2101.00127},
eprintclass = {math.CO},
eprinttype = {arXiv},
keywords = {math.CO, cs.LO, 05-04 (Primary) 05C70, 68R05 (Secondary)}
}
@Article{ Hall1935,
author = {P. Hall},
journal = {Journal of the London Mathematical Society},
title = {On Representatives of Subsets},
year = {1935},
month = {jan},
number = {1},
pages = {26--30},
volume = {s1-10},
doi = {10.1112/jlms/s1-10.37.26},
publisher = {Wiley}
}
@Book{ halmos1950measure,
author = {Halmos, Paul R},
title = {Measure theory},
publisher = {Springer-Verlag New York},
year = 1950,
isbn = {978-1-4684-9440-2},
doi = {10.1007/978-1-4684-9440-2}
}
@Book{ halmos2013measure,
title = {Measure theory},
author = {Halmos, Paul R},
volume = {18},
year = {1950},
publisher = {Springer},
isbn = {0-387-90088-8}
}
@Book { har77,
author = {Hartshorne, Robin},
title = {Algebraic geometry},
note = {Graduate Texts in Mathematics, No. 52},
publisher = {Springer-Verlag, New York-Heidelberg},
year = {1977},
pages = {xvi+496},
isbn = {0-387-90244-9},
mrclass = {14-01},
mrnumber = {0463157},
mrreviewer = {Robert Speiser},
}
@Book{ hardy2008introduction,
title = {An Introduction to the Theory of Numbers},
author = {Hardy, GH and Wright, EM and Heath-Brown, Roger and
Silverman, Joseph},
year = {2008},
publisher = {Oxford University Press}
}
@Article{ Haze09,
title = {Witt vectors. Part 1},
isbn = {9780444532572},
issn = {1570-7954},
url = {http://dx.doi.org/10.1016/S1570-7954(08)00207-6},
doi = {10.1016/s1570-7954(08)00207-6},
journal = {Handbook of Algebra},
publisher = {Elsevier},
author = {Hazewinkel, Michiel},
year = {2009},
pages = {319–472}
}
@Article{ Higman52,
author = {Higman, Graham},
title = {Ordering by Divisibility in Abstract Algebras},
journal = {Proceedings of the London Mathematical Society},
volume = {s3-2},
number = {1},
pages = {326-336},
doi = {https://doi.org/10.1112/plms/s3-2.1.326},
year = {1952}
}
@Book{ Hofstadter-1979,
author = "Douglas R Hofstadter",
title = "{{G}ödel, {E}scher, {B}ach: an eternal golden braid}",
publisher = "Basic Books",
address = "New York, NY",
series = "Penguin books",
year = "1979"
}
@Book{ HubbardWest-ode,
author = {John H. Hubbard and Beverly H. West},
title = {Differential Equations: A Dynamical Systems Approach},
subtitle = {Ordinary Differential Equations},
year = {1991},
publisher = {Springer},
location = {New York},
volume = {5},
isbn = {978-1-4612-8693-6},
doi = {10.1007/978-1-4612-4192-8},
pages = {XX, 350}
}
@Article{ huneke2002,
author = {Huneke, Craig},
title = {The Friendship Theorem},
publisher = {Mathematical Association of America},
year = {2002},
pages = {192--194},
journal = {The American Mathematical Monthly},
issn = {00029890, 19300972},
volume = {109},
number = {2},
doi = {10.1080/00029890.2002.11919853},
url = {https://doi.org/10.1080/00029890.2002.11919853}
}
@Book{ james1999,
author = {James, Ioan},
title = {Topologies and uniformities},
series = {Springer Undergraduate Mathematics Series},
note = {Revised version of {{\i}t Topological and uniform spaces}
[Springer, New York, 1987; MR0884154 (89b:54001)]},
publisher = {Springer-Verlag London, Ltd., London},
year = {1999},
pages = {xvi+230},
isbn = {1-85233-061-9},
mrclass = {54-01 (54A05 54E15)},
mrnumber = {1687407},
mrreviewer = {Hans-Peter A. K\"{u}nzi},
doi = {10.1007/978-1-4471-3994-2},
url = {https://doi.org/10.1007/978-1-4471-3994-2}
}
@Article{ joyal1977,
author = {André Joyal},
title = {Remarques sur la théorie des jeux à deux personnes},
journal = {Gazette des Sciences Mathematiques du Québec},
volume = {1},
number = {4},
pages = {46--52},
year = {1977},
note = {(English translation at
https://bosker.files.wordpress.com/2010/12/joyal-games.pdf)}
}
@Article{ Joyce1982,
author = {David Joyce},
title = {A classifying invariant of knots, the knot quandle},
journal = {Journal of Pure and Applied Algebra},
year = {1982},
volume = {23},
number = {1},
month = {1},
pages = {37--65},
doi = {10.1016/0022-4049(82)90077-9},
publisher = {Elsevier {BV}}
}
@InProceedings{ lewis2019,
author = {Lewis, Robert Y.},
title = {A Formal Proof of {H}ensel's Lemma over the {$p$}-adic
Integers},
booktitle = {Proceedings of the 8th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
series = {CPP 2019},
year = {2019},
isbn = {978-1-4503-6222-1},
location = {Cascais, Portugal},
pages = {15--26},
numpages = {12},
url = {http://doi.acm.org/10.1145/3293880.3294089},
doi = {10.1145/3293880.3294089},
acmid = {3294089},
publisher = {ACM},
address = {New York, NY, USA},
keywords = {Hensel's lemma, Lean, formal proof, p-adic}
}
@Book{ LurieSAG,
title = {Spectral Algebraic Geometry},
author = {Jacob Lurie},
url = {https://www.math.ias.edu/~lurie/papers/SAG-rootfile.pdf},
year = {last updated 2018}
}
@Book{ marcus1977number,
title = {Number fields},
author = {Marcus, Daniel A and Sacco, Emanuele},
volume = {2},
year = {1977},
publisher = {Springer}
}
@InProceedings{ mcbride1996,
title = {Inverting inductively defined relations in {LEGO}},
author = {McBride, Conor},
booktitle = {International Workshop on Types for Proofs and Programs},
pages = {236--253},
year = {1996},
organization = {Springer}
}
@Book{ MM92,
title = {Sheaves in geometry and logic: A first introduction to
topos theory},
author = {MacLane, Saunders and Moerdijk, Ieke},
year = {1992},
publisher = {Springer Science \& Business Media}
}
@Article{ MR0236876,
title = {A new proof that metric spaces are paracompact},
author = {Mary Ellen Rudin},
year = 1969,
journal = {Proc. Amer. Math. Soc.},
volume = {20},
pages = {603},
mrnumber = {0236876},
doi = {10.1090/S0002-9939-1969-0236876-3}
}
@Article{ MR1167694,
author = {Blass, Andreas},
title = {A game semantics for linear logic},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {56},
year = {1992},
number = {1-3},
pages = {183--220},
issn = {0168-0072},
mrclass = {03B70 (68Q55)},
mrnumber = {1167694},
mrreviewer = {Fangmin Song},
doi = {10.1016/0168-0072(92)90073-9},
url = {https://doi.org/10.1016/0168-0072(92)90073-9}
}
@Book{ MR1237403,
author = {Lidl, R. and Mullen, G. L. and Turnwald, G.},
title = {Dickson polynomials},
series = {Pitman Monographs and Surveys in Pure and Applied
Mathematics},
volume = {65},
publisher = {Longman Scientific \& Technical, Harlow; copublished in
the United States with John Wiley \& Sons, Inc., New York},
year = {1993},
pages = {vi+207},
isbn = {0-582-09119-5},
mrclass = {11T06 (12E05 13B25 33C80 94A60)},
mrnumber = {1237403},
mrreviewer = {S. D. Cohen}
}
@Article{ MR317916,
author = {Davis, Martin},
title = {Hilbert's tenth problem is unsolvable},
journal = {Amer. Math. Monthly},
fjournal = {American Mathematical Monthly},
volume = {80},
year = {1973},
pages = {233--269},
issn = {0002-9890},
mrclass = {02G05 (10B99 10N05)},
mrnumber = {317916},
mrreviewer = {R. L. Goodstein},
doi = {10.2307/2318447},
url = {https://doi.org/10.2307/2318447}
}
@Article{ MR32592,
author = {Motzkin, Th.},
title = {The {E}uclidean algorithm},
journal = {Bull. Amer. Math. Soc.},
fjournal = {Bulletin of the American Mathematical Society},
volume = {55},
year = {1949},
pages = {1142--1146},
issn = {0002-9904},
mrclass = {09.1X},
mrnumber = {32592},
mrreviewer = {B. N. Moyls},
doi = {10.1090/S0002-9904-1949-09344-8},
url = {https://doi.org/10.1090/S0002-9904-1949-09344-8}
}
@Article{ MR3790629,
author = {Bell, J. S.},
title = {On the {E}instein {P}odolsky {R}osen paradox},
journal = {Phys. Phys. Fiz.},
fjournal = {Physics Physique Fizika},
volume = {1},
year = {1964},
number = {3},
pages = {195--200},
issn = {0554-128X},
mrclass = {DML},
mrnumber = {3790629},
doi = {10.1103/PhysicsPhysiqueFizika.1.195},
url = {https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195}
}
@Article{ MR399081,
author = {Hiblot, Jean-Jacques},
title = {Des anneaux euclidiens dont le plus petit algorithme n'est
pas \`a valeurs finies},
journal = {C. R. Acad. Sci. Paris S\'{e}r. A-B},
fjournal = {Comptes Rendus Hebdomadaires des S\'{e}ances de
l'Acad\'{e}mie des Sciences. S\'{e}ries A et B},
volume = {281},
year = {1975},
number = {12},
pages = {Ai, A411--A414},
issn = {0151-0509},
mrclass = {13F15 (12A20)},
mrnumber = {399081},
mrreviewer = {N. Sankaran}
}
@InCollection{ MR541021,
author = {Nagata, Masayoshi},
title = {On {E}uclid algorithm},
booktitle = {C. {P}. {R}amanujam---a tribute},
series = {Tata Inst. Fund. Res. Studies in Math.},
volume = {8},
pages = {175--186},
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publisher = {Tsing Hua University, Department of Mathematics, Hsinchu},
language = {English},
msc2010 = {41A58 30K05},
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