References

[AGM94] S. Abramsky, D. M. Gabbay, T. S. E. Maibaum, editors. Handbook of logic in computer science. Vol. 3: Semantic structures. Oxford: Clarendon Press, 1994. ISBN 0-19-853762-X. Zbl:0829.68111. [1] [2] [3]
[ARV10] J. Adámek, J. Rosický, E. M. Vitale. Algebraic Theories: A Categorical Introduction to General Algebra. Cambridge Tracts in Mathematics. Cambridge University Press, 2010. [1]
[AR94] Jiří Adámek, Jiří Rosický. Locally presentable and accessible categories. Volume 189 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1994. ISBN 0-521-42261-2. doi:10.1017/CBO9780511600579, MR:1294136, URL: https://doi.org/10.1017/CBO9780511600579. [1] [2]
[AL19] Benedikt Ahrens, Peter LeFanu Lumsdaine. Displayed Categories. Logical Methods in Computer Science, 2019. doi:10.23638/LMCS-15(1:20)2019. [1]
[Aig97] Martin Aigner. Combinatorial theory. Classics in Mathematics. Springer-Verlag, Berlin, 1997. ISBN 3-540-61787-6. Reprint of the 1979 original. doi:10.1007/978-3-642-59101-3, MR:1434477, URL: https://doi.org/10.1007/978-3-642-59101-3. [1]
[AZ98] Martin Aigner, Günter M. Ziegler. Proofs from THE BOOK. Berlin: Springer, 1998. ISBN 3-540-63698-6. Zbl:0905.00001. [1] [2]
[AHCF12] Elad Aigner-Horev, Johannes Carmesin, Jan-Oliver Fröhlich. Infinite matroid union. 2012. arXiv:1111.0602. [1] [2]
[AE72] Erik M. Alfsen, Edward G. Effros. Structure in real Banach spaces. I and II. Ann. Math. (2), 96:98–173, 1972. doi:10.2307/1970895, Zbl:0248.46019. [1]
[AS03] Erik M. Alfsen, Frederic W. Shultz. Geometry of state spaces of operator algebras. Boston, MA: Birkhäuser, 2003. ISBN 0-8176-4319-2. Zbl:1042.46001. [1]
[AK21] A. Altman, S. Kleiman. A Term of Commutative Algebra. Worldwide Center of Mathematics, 2021. ISBN 9780988557215. [1] [2] [3] [4] [5] [6] [7]
[Alu16] Paolo Aluffi. Algebra: Chapter 0. Reprinted with corrections by the American Mathematical Society edition. Volume 104 of Graduate Studies in Mathematics. American Mathematical Society, 2016. [1]
[AM69] M. F. Atiyah, I. G. Macdonald. Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR:0242802. [1] [2] [3] [4] [5] [6]
[ACH19] Jeremy Avigad, Mario M. Carneiro, Simon Hudon. Data Types as Quotients of Polynomial Functors. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving, ITP 2019, September 9-12, 2019, Portland, OR, USA, volume 141 of LIPIcs, 6:1–6:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. doi:10.4230/LIPIcs.ITP.2019.6, URL: https://doi.org/10.4230/LIPIcs.ITP.2019.6. [1] [2] [3] [4] [5] [6] [7] [8]
[AdMK17] Jeremy Avigad, Leonardo de Moura, Soonho Kong. Theorem Proving in Lean. 2017. URL: https://leanprover.github.io/theorem_proving_in_lean/. [1]
[Axl15] Sheldon Axler. Linear algebra done right. 3rd ed. 3rd ed. Springer, 2015. ISBN 978-3-319-11079-0/hbk; 978-3-319-11080-6/ebook. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
[Ban] Banasiak. Banach Lattices in Applications. University of Pretoria, Pretoria, South Africa. [1] [2]
[Bar67] Donald W. Barnes. On Cartan subalgebras of Lie algebras. Math. Z., 101:350–355, 1967. doi:10.1007/BF01109800, MR:220785, URL: https://doi.org/10.1007/BF01109800. [1] [2] [3] [4] [5] [6]
[BH19] Clark Barwick, Peter Haine. Pyknotic objects, I. Basic notions. 2019. arXiv:1904.09966. [1]
[Bas73] Hyman Bass. Unitary algebraic K-theory. In Hyman Bass, editor, Hermitian K-Theory and Geometric Applications, 57–265. Berlin, Heidelberg, 1973. Springer Berlin Heidelberg. [1]
[Bea04] Richard Beals. Analysis. An introduction. Cambridge University Press, 2004. ISBN 0521600472.
[BW93] Thomas Becker, Volker Weispfenning. Gröbner Bases. Volume 141 of Graduate Texts in Mathematics. Springer New York, New York, NY, 1993. ISBN 978-1-4612-6944-1. doi:10.1007/978-1-4612-0913-3, URL: http://link.springer.com/10.1007/978-1-4612-0913-3. [1] [2] [3] [4]
[Beh79] Ehrhard Behrends. M-structure and the Banach-Stone theorem. Volume 736. Springer, Cham, 1979. Zbl:0436.46013. [1]
[BBDG18] A. A. Beilinson, J. Bernstein, P. Deligne, O. Gabber. Analyse et topologie sur les espaces singuliers. I : Faisceaux pervers. Volume 100 of Astérisque. Société Mathématique de France, Paris, 2018. MR:751965. [1]
[BF93] R. Keith Dennis Benson Farb. Noncommutative Algebra. Volume 144 of Graduate Texts in Mathematics. Springer, 1993. URL: https://link.springer.com/book/10.1007/978-1-4612-0889-1. [1]
[Ber85] Vitaly Bergelson. Sets of Recurrence of Zm-Actions and Properties of Sets of Differences in Zm. Journal of the London Mathematical Society, s2-31(2):295-304, 1985. doi:10.1112/jlms/s2-31.2.295, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/jlms/s2-31.2.295, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s2-31.2.295. [1]
[Ber87] Marcel Berger. Geometry I. First edition. Universitext. Springer Berlin, Heidelberg, 1987. [1]
[BL76] Jöran Bergh, Jörgen Löfström. Interpolation Spaces. Springer Berlin, 1976. [1]
[Ber12] S. Bernstein. Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités. Comm. Kharkov Math. Soc., 1912.
[Ber74] Pierre Berthelot. Cohomologie Cristalline Des Schémas de Caractéristique $p>0$. Number 407 in Lecture Notes in Mathematics. sv, 1974. [1] [2] [3]
[BO78] Pierre Berthelot, Arthur Ogus. Notes on Crystalline Cohomology. Number 21 in Math. Notes. pup, 1978. [1]
[BD96] Ilya Beylin, Peter Dybjer. Extracting a proof of coherence for monoidal categories from a proof of normalization for monoids. In Stefano Berardi, Mario Coppo, editors, Types for Proofs and Programs, 47–61. Berlin, Heidelberg, 1996. Springer Berlin Heidelberg. [1] [2]
[Bil99] Patrick Billingsley. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. John Wiley & Sons, Inc., New York, 1999. ISBN 0-471-19745-9. A Wiley-Interscience Publication. doi:10.1002/9780470316962, MR:1700749, URL: https://doi.org/10.1002/9780470316962. [1] [2] [3] [4]
[Bir37] Garrett Birkhoff. Rings of sets. Duke Mathematical Journal, 3(3):443–454, 1937. doi:10.1215/S0012-7094-37-00334-X, URL: https://doi.org/10.1215/S0012-7094-37-00334-X. [1]
[Bir42] Garrett Birkhoff. Lattice-Ordered groups. Ann. of Math. (2), 43:298–331, 1942. doi:10.2307/1968871, MR:6550, URL: https://doi.org/10.2307/1968871. [1] [2] [3] [4]
[BB05] Anders Björner, Francesco Brenti. Combinatorics of Coxeter groups. Volume 231 of Graduate Texts in Mathematics. Springer, New York, 2005. ISBN 978-3540-442387; 3-540-44238-3. MR:2133266.
[Bog07] V. I. Bogachev. Measure theory. Vol. I, II. Springer-Verlag, Berlin, 2007. ISBN 978-3-540-34513-8; 3-540-34513-2. doi:10.1007/978-3-540-34514-5, URL: https://doi.org/10.1007/978-3-540-34514-5. [1]
[Boj74] Ranko Bojanić. A simple proof of Mahler's theorem on approximation of continuous functions of a p-adic variable by polynomials. Journal of Number Theory, 6:412-415, 1974. doi:10.1016/0022-314X(74)90038-9, URL: https://doi.org/10.1016/0022-314X(74)90038-9. [1] [2]
[Bol86] Béla Bollobás. Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability. Cambridge University Press, 1986. ISBN 0521330599. [1] [2]
[Bor94a] Francis Borceux. Handbook of Categorical Algebra: Volume 1, Basic Category Theory. Volume 50 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3] [4]
[Bor94b] Francis Borceux. Handbook of Categorical Algebra: Volume 2, Categories and Structures. Volume 51 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3] [4] [5] [6] [7] [8]
[Bor94c] Francis Borceux. Handbook of Categorical Algebra: Volume 3, Sheaf Theory. Volume 52 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3]
[Bor86] Richard Borcherds. Vertex algebras, Kac-Moody algebras, and the monster. Proceedings of the National Academy of Sciences of the United States of America, 83(10):3068–3071, 1986. doi:10.1073/pnas.83.10.3068. [1]
[BJ24] James Borger, Jaiung Jun. Facets of module theory over semirings. 2024. arXiv:2405.18645, URL: https://arxiv.org/abs/2405.18645.
[BGR84] S. Bosch, U. Güntzer, R. Remmert. Non-Archimedean Analysis : A Systematic Approach to Rigid Analytic Geometry. Volume 261 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag Berlin, 1984. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[Bou87] N. Bourbaki. Topological vector spaces. Chapters 1–5. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1987. ISBN 3-540-13627-4. Translated from the French by H. G. Eggleston and S. Madan. doi:10.1007/978-3-642-61715-7, MR:910295, URL: https://doi.org/10.1007/978-3-642-61715-7. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
[Bou90] N. Bourbaki. Algebra. II. Chapters 4–7. Elements of Mathematics. Springer-Verlag, Berlin, 1990. ISBN 3-540-19375-8. Translated from the French by P. M. Cohn and J. Howie. MR:1080964. [1] [2] [3] [4] [5] [6] [7] [8]
[Bou98a] N. Bourbaki. Algebra. I. Chapters 1–3. Softcover edition of the 2nd printing 1989. Elements of Mathematics. Springer-Verlag, Berlin, 1998. ISBN 3-540-64243-9. Translated from the French. [1] [2] [3] [4] [5]
[Bou23] N. Bourbaki. Théories Spectrales. Chapitres 3 à 5. Number 1 in Éléments de mathématique. Springer Cham, 2023. ISBN 978-3-031-19504-4. URL: https://doi.org/10.1007/978-3-031-19505-1. [1]
[Bou66a] Nicolas Bourbaki. Elements of mathematics. General topology. Part 1. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR:0205210. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
[Bou66b] Nicolas Bourbaki. Elements of mathematics. General topology. Part 2. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR:979295. [1] [2] [3] [4]
[Bou98b] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 1–3. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1998. ISBN 3-540-64242-0. Translated from the French, Reprint of the 1989 English translation. MR:1728312.
[Bou02] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 4–6. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2002. ISBN 3-540-42650-7. Translated from the 1968 French original by Andrew Pressley. MR:1890629. [1] [2] [3] [4] [5] [6] [7] [8]
[Bou05] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 7–9. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2005. ISBN 3-540-43405-4. Translated from the 1975 and 1982 French originals by Andrew Pressley. MR:2109105.
[Bou07] Nicolas Bourbaki. Algèbre. Chapitre IX. Réimpression inchangée de l'édition originale de 1959. Number 2 in Eléments de mathématique. Springer, 2007. ISBN 978-3-540-35338-6. [1] [2] [3] [4]
[BG15] Nathan Bowler, Stefan Geschke. Self-dual uniform matroids on infinite sets. Proceedings of the American Mathematical Society, 144:1, Oct 2015. doi:10.1090/proc/12667.
[BV04] Stephen P. Boyd, Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. ISBN 978-0-521-83378-3. URL: https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf. [1]
[BS13] M. P. Brodmann, R. Y. Sharp. Local cohomology. Second edition. Volume 136 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2013. ISBN 978-0-521-51363-0. An algebraic introduction with geometric applications. [1]
[BDK+13] Henning Bruhn, Reinhard Diestel, Matthias Kriesell, Rudi Pendavingh, Paul Wollan. Axioms for infinite matroids. Advances in Mathematics, 239:18-46, 2013. doi:10.1016/j.aim.2013.01.011, URL: https://www.sciencedirect.com/science/article/pii/S0001870813000261.
[Buz01] Raushan Z. Buzyakova. On clopen sets in Cartesian products. Comment. Math. Univ. Carolin., 42(2):357–362, 2001. MR:1832154. [1] [2] [3]
[CGRP14] Miguel Cabrera García, Ángel Rodríguez Palacios. Non-associative normed algebras. Volume 1. The Vidav-Palmer and Gelfand-Naimark theorems. Volume 154. Cambridge: Cambridge University Press, 2014. ISBN 978-1-107-04306-0; 978-1-107-33776-3. doi:10.1017/CBO9781107337763, Zbl:1322.46003. [1] [2] [3]
[CM72] Jean Marie Cadiou Cadiou, Zohar Manna. Recursive definitions of partial functions and their computations. ACM SIGACT News, pages 58–65, Jan 1972. doi:10.1145/942580.807072. [1]
[Cal00] Grigore Cǎlugǎreanu. Lattice Concepts of Module Theory. Jan 2000. doi:10.1007/978-94-015-9588-9. [1] [2] [3] [4]
[Car20] Olivia Caramello. Denseness conditions, morphisms and equivalences of toposes. 2020. arXiv:1906.08737, URL: https://arxiv.org/abs/1906.08737. [1]
[CLW93] Aurelio Carboni, Stephen Lack, R.F.C. Walters. Introduction to extensive and distributive categories. Journal of Pure and Applied Algebra, 84(2):145-158, 1993. doi:10.1016/0022-4049(93)90035-R, URL: https://www.sciencedirect.com/science/article/pii/002240499390035R. [1]
[Car15] Mario Carneiro. Arithmetic in Metamath, Case Study: Bertrand's Postulate. arXiv preprint arXiv:1503.02349, 2015. [1]
[Car18] Mario Carneiro. A Lean formalization of Matiyasevič's theorem. 2018. arXiv:1802.01795. [1] [2]
[Car19] Mario M. Carneiro. Formalizing Computability Theory via Partial Recursive Functions. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving, ITP 2019, September 9-12, 2019, Portland, OR, USA, volume 141 of LIPIcs, 12:1–12:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. doi:10.4230/LIPIcs.ITP.2019.12, URL: https://doi.org/10.4230/LIPIcs.ITP.2019.12. [1] [2] [3] [4]
[CE56] Henri Cartan, Samuel Eilenberg. Homological algebra. Princeton University Press, Princeton, NJ, 1956. MR:77480. [1]
[Car05] R. W. Carter. Lie algebras of finite and affine type. Volume 96 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2005. ISBN 978-0-521-85138-1; 0-521-85138-6. doi:10.1017/CBO9780511614910, MR:2188930, URL: https://doi.org/10.1017/CBO9780511614910. [1] [2]
[Cas50] J. W. S. Cassels. Some metrical theorems in Diophantine approximation. I. Proc. Cambridge Philos. Soc., 46:209–218, 1950. doi:10.1017/s0305004100025676, MR:36787, URL: https://doi.org/10.1017/s0305004100025676.
[Cas86] J. W. S. Cassels. Local Fields. London Mathematical Society Student Texts. Cambridge University Press, 1986. doi:10.1017/CBO9781139171885. [1]
[CF67] John William Scott Cassels, Albrecht Fröhlich. Algebraic number theory. Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[Cha96] Robin Chapman. A Polynomial Taking Integer Values. Math. Mag., 69(2):121–121, 1996.
[Chi20] Vineeth Chintala. Sorry, the Nilpotents Are in the Center. Jun 2020. doi:10.48550/arXiv.1805.11451, arXiv:1805.11451. [1]
[Cho94] Ching-Tsun Chou. A formal theory of undirected graphs in higher-order logic. In Thomas F. Melham, Juanito Camilleri, editors, Higher Order Logic Theorem Proving and Its Applications, 144–157. Berlin, Heidelberg, 1994. Springer Berlin Heidelberg. [1] [2] [3]
[Chu12] Cho-Ho Chu. Jordan structures in geometry and analysis. Volume 190. Cambridge: Cambridge University Press, 2012. ISBN 978-1-107-01617-0. Zbl:1238.17001. [1]
[Cla] Pete L. Clark. Geometry of Numbers with Applications to Number Theory. URL: http://alpha.math.uga.edu/~pete/geometryofnumbers.pdf. [1]
[CCC+12] David A. Cohen, Martin C. Cooper, Páidí Creed, Peter G. Jeavons, Stanislav Živný. An Algebraic Theory of Complexity for Discrete Optimisation. CoRR, 2012. arXiv:1207.6692, URL: http://arxiv.org/abs/1207.6692. [1]
[Coh13] Donald L. Cohn. Measure Theory: Second Edition. Birkhäuser Advanced Texts Basler Lehrbücher. Springer New York, New York, NY, 2013. ISBN 9781461469551 9781461469568. doi:10.1007/978-1-4614-6956-8, URL: https://link.springer.com/10.1007/978-1-4614-6956-8. [1]
[Coh95] P. M. Cohn. Skew Fields: Theory of General Division Rings. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1995. doi:10.1017/CBO9781139087193. [1]
[Col10] Pierre Colmez. Fonctions d'une variable p-adique. Asterisque, 330:13–59, 2010. URL: http://www.numdam.org/article/AST_2010__330__13_0.pdf. [1] [2]
[CL21] Johan Commelin, Robert Y. Lewis. Formalizing the Ring of Witt Vectors. In Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2021, 264–277. New York, NY, USA, 2021. Association for Computing Machinery. doi:10.1145/3437992.3439919, URL: https://doi.org/10.1145/3437992.3439919. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[Con00] Brian Conrad. Grothendieck duality and base change. Volume 1750 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2000. ISBN 3-540-41134-8. doi:10.1007/b75857, MR:1804902, URL: https://doi.org/10.1007/b75857. [1] [2] [3] [4] [5] [6]
[Cona] K. Conrad. Ostrowski for number fields. URL: https://kconrad.math.uconn.edu/blurbs/gradnumthy/ostrowskinumbfield.pdf. [1]
[Conb] K. Conrad. Ostrowski's Theorem for Q. URL: https://kconrad.math.uconn.edu/blurbs/gradnumthy/ostrowskiQ.pdf. [1]
[Con01] J. H. Conway. On numbers and games. Second edition. A K Peters, Ltd., Natick, MA, 2001. ISBN 1-56881-127-6. MR:1803095. [1] [2] [3]
[Con90] John B. Conway. A course in functional analysis. 2nd ed. Volume 96 of Grad. Texts Math. New York etc.: Springer-Verlag, 1990. ISBN 0-387-97245-5. Zbl:0706.46003. [1]
[CC79] P. Cousot, R. Cousot. Constructive Versions of Tarski's Fixed Point Theorems. Pacific Journal of Mathematics, 81(1):43–57, 1979. [1] [2]
[CLOS97] David A. Cox, John Little, Donal O'Shea. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.). Undergraduate texts in mathematics. Springer, 1997. ISBN 978-0-387-94680-1. [1] [2]
[CMP17] Alissa S. Crans, Sujoy Mukherjee, Józef H. Przytycki. On homology of associative shelves. J. Homotopy Relat. Struct., 12(3):741–763, 2017. doi:10.1007/s40062-016-0164-9, MR:3691304, URL: https://doi.org/10.1007/s40062-016-0164-9. [1]
[DP02] B. A. Davey, H. A. Priestley. Introduction to lattices and order. Second edition. Cambridge University Press, New York, 2002. ISBN 0-521-78451-4. doi:10.1017/CBO9780511809088, MR:1902334, URL: https://doi.org/10.1017/CBO9780511809088. [1] [2] [3]
[Day72] Brian Day. A reflection theorem for closed categories. J. Pure Appl. Algebra, 2(1):1–11, 1972. doi:10.1016/0022-4049(72)90021-7, URL: https://doi.org/10.1016/0022-4049(72)90021-7. [1]
[dMKA+15] Leonardo de Moura, Soonho Kong, Jeremy Avigad, Floris van Doorn, Jakob von Raumer. The Lean Theorem Prover (System Description). In Amy P. Felty, Aart Middeldorp, editors, Automated Deduction - CADE-25, 378–388. Cham, 2015. Springer International Publishing.
[DP89] Valeria De Paiva. The Dialectica categories. Jan 1989. doi:10.1090/conm/092/1003194, URL: https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-213.pdf. [1] [2]
[Del75] P. Deligne. Courbes elliptiques: formulaire d'après J. Tate. In Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), 53–73. Lecture Notes in Math., Vol. 476. 1975. MR:0387292. [1]
[Dem70] Michel Demazure. Exposé XXI, Données Radicielles. In A. Grothendieck M. Demazure, editor, Séminaire de Géométrie Algébrique du Bois Marie - 1962-64 - Schémas en groupes - (SGA 3) - vol. 3, Structure des Schémas en Groupes Reductifs, volume 153 of Lecture Notes in Mathematics, 85–155. Springer-Verlag, 1970. URL: https://wstein.org/sga/SGA3/Expo21-alpha.pdf. [1] [2]
[DeML78] Richard A. DeMillo, Richard J. Lipton. A probabilistic remark on algebraic program testing. Information Processing Letters, 7(4):193–195, 1978. doi:10.1016/0020-0190(78)90067-4. [1]
[Die53] Jean Dieudonné. On semi-simple Lie algebras. Proc. Amer. Math. Soc., 4:931–932, 1953. doi:10.2307/2031832, MR:59262, URL: https://doi.org/10.2307/2031832. [1]
[Djo73] D. Ž. Djoković. Epimorphisms of modules which must be isomorphisms. Canad. Math. Bull., 16:513–515, 1973. doi:10.4153/CMB-1973-083-0, MR:346014, URL: https://doi.org/10.4153/CMB-1973-083-0. [1] [2] [3] [4] [5] [6]
[Dol76] S. W. Dolan. A Proof of Jacobson's Theorem. Canadian Mathematical Bulletin, 19(1):59–61, Mar 1976. doi:10.4153/CMB-1976-007-9.
[Dol58] Albrecht Dold. Homology of symmetric products and other functors of complexes. Ann. of Math. (2), 68:54–80, 1958. doi:10.2307/1970043, MR:97057. [1] [2] [3]
[DRS72] Peter Doubilet, Gian-Carlo Rota, Richard Stanley. On the foundations of combinatorial theory. VI. The idea of generating function. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, 267–318. Univ. California Press, Berkeley, CA, 1972. MR:403987. [1]
[DLM22] Frédéric Dupuis, Robert Y. Lewis, Heather Macbeth. Formalized functional analysis with semilinear maps. 2022. arXiv:2202.05360. [1] [2] [3]
[Dyc92] Roy Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 57(3):795–807, 1992. doi:10.2307/2275431. [1]
[Ech05] Federico Echenique. A short and constructive proof of Tarski’s fixed-point theorem. International Journal of Game Theory, 33(2):215–218, 2005. doi:10.1007/s001820400192. [1] [2]
[EW17] Manfred Einsiedler, Thomas Ward. Functional Analysis, Spectral Theory, and Applications. Springer, 2017. doi:10.1007/978-3-319-58540-6. [1]
[Eis95] David Eisenbud. Commutative algebra. Graduate Texts in Mathematics. Springer, New York, NY, Mar 1995. ISBN 978-0-387-94268-1. doi:10.1007/978-1-4612-5350-1.
[Ell06] Jesse Elliott. Binomial rings, integer-valued polynomials, and λ-rings. Journal of Pure and Applied Algebra, 207(1):165–185, 2006. doi:10.1016/j.jpaa.2005.09.003. [1] [2]
[Eng97] Konrad Engel. Sperner theory. Cambridge University Press, 1997. [1] [2]
[Eng89] Ryszard Engelking. General topology. Second edition. Volume 6 of Sigma Series in Pure Mathematics. Heldermann Verlag, Berlin, 1989. ISBN 3-88538-006-4. Translated from the Polish by the author. MR:1039321. [1]
[ERS66] P. Erdös, A. Rényi, V. Sós. On a problem of graph theory. Studia Sci. Math., pages 215–235, 1966. URL: https://www.renyi.hu/~p_erdos/1966-06.pdf. [1]
[Ete81] Nasrollah Etemadi. An elementary proof of the strong law of large numbers. Z. Wahrsch. Verw. Gebiete, 55(1):119–122, 1981. doi:10.1007/BF01013465, MR:606010, URL: https://doi.org/10.1007/BF01013465. [1]
[EGNO15] Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik. Tensor Categories. American Mathematical Society (AMS), Providence, RI, 2015. ISBN 978-1-4704-3441-0. [1]
[Fed96] Herbert Federer. Geometric Measure Theory. Classics in Mathematics. Springer-Verlag Berlin Heidelberg, 1996. doi:10.1007/978-3-642-62010-2. [1] [2] [3] [4]
[FR92] Roger Fenn, Colin Rourke. Racks and links in codimension two. Journal of Knot Theory and its Ramifications, 1(4):343–406, 1992. doi:10.1142/S0218216592000203, MR:1194995. [1]
[Fie71] David E. Fields. Zero divisors and nilpotent elements in power series rings. Proceedings of the American Mathematical Society, 27(3):427–433, 1971. doi:10.1090/S0002-9939-1971-0271100-6. [1]
[Fre03] David H. Fremlin. Measure theory. Vol. 4. Torres Fremlin, Colchester, 2003. Topological Measure Spaces. [1] [2] [3]
[Fre10] David H. Fremlin. Measure theory. Vol. 2. Torres Fremlin, Colchester, 2010. ISBN 0-9538129-2-8. Broad foundations, 2010 edition. [1] [2] [3] [4]
[Fre57] Jean Frenkel. Cohomologie non abélienne et espaces fibrés. Bull. Soc. Math. France, 85:135–220, 1957. MR:98200, URL: http://www.numdam.org/item?id=BSMF_1957__85__135_0. [1]
[Fre64] Peter J Freyd. Abelian categories. Harper's Series in Modern Mathematics. Harper & Row New York, 1964. [1]
[Fri05] Yaakov Friedman. Physical applications of homogeneous balls. With the assistance of Tzvi Scarr. Volume 40. Boston, MA: Birkhäuser, 2005. ISBN 0-8176-3339-1. Zbl:1080.46001. [1]
[FP90] Rudolf Fritsch, Renzo Piccinini. Cellular Structures in Topology. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1990. doi:10.1017/CBO9780511983948, URL: https://doi.org/10.1017/CBO9780511983948. [1]
[Fuc63] L. Fuchs. Partially ordered algebraic systems. Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR:0171864. [1] [2] [3]
[FH04] William Fulton, Joe Harris. Representation theory: a first course. Springer, 2004. [1]
[FL94] Zoltán Füredi, Peter A. Loeb. On the best constant for the Besicovitch covering theorem. Proc. Am. Math. Soc., 121(4):1063–1073, 1994. doi:10.2307/2161215, Zbl:0802.28002. [1]
[FLST20] Basil Fürer, Andreas Lochbihler, Joshua Schneider, Dmitriy Traytel. Quotients of Bounded Natural Functors. In Nicolas Peltier, Viorica Sofronie-Stokkermans, editors, Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Paris, France, July 1-4, 2020, Proceedings, Part II, volume 12167 of Lecture Notes in Computer Science, 58–78. Springer, 2020. doi:10.1007/978-3-030-51054-1_4, URL: https://doi.org/10.1007/978-3-030-51054-1_4.
[GZ67] P. Gabriel, M. Zisman. Calculus of fractions and homotopy theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. Springer-Verlag New York, Inc., New York, 1967. [1] [2] [3]
[Gal61] Patrick Gallagher. Approximation by reduced fractions. J. Math. Soc. Japan, 13:342–345, 1961. doi:10.2969/jmsj/01340342, MR:133297, URL: https://doi.org/10.2969/jmsj/01340342. [1]
[GQ11] J. Gallier, J. Quaintance. Notes on Differential Geometry and Lie Groups. In 2011. URL: https://www.cis.upenn.edu/~cis610/diffgeom-n.pdf. [1]
[GM] B. Gärtner, J. Matousek. Cone Programming. URL: https://ti.inf.ethz.ch/ew/lehre/ApproxSDP09/notes/conelp.pdf. [1]
[Ghy87] Étienne Ghys. Groupes d'homéomorphismes du cercle et cohomologie bornée. Contemporary Mathematics, 58(III):81-106, 1987. doi:10.1090/conm/058.3/893858. [1] [2] [3] [4] [5] [6] [7]
[GO09] Jeremy Gibbons, BRUNO C. d. S. Oliveira. The essence of the Iterator pattern. Journal of Functional Programming, 19(3-4):377–402, Jul 2009. doi:10.1017/S0956796809007291, URL: https://www.cambridge.org/core/product/identifier/S0956796809007291/type/journal_article. [1]
[GHK+80] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, Dana S. Scott. A compendium of continuous lattices. Springer-Verlag, Berlin-New York, 1980. ISBN 3-540-10111-X. MR:614752. [1] [2] [3] [4] [5] [6]
[Gle58] Andrew M. Gleason. Projective topological spaces. Illinois J. Math., 2:482–489, 1958. MR:121775, URL: http://projecteuclid.org/euclid.ijm/1255454110. [1] [2] [3] [4] [5] [6]
[GJ09] Paul G. Goerss, John F. Jardine. Simplicial homotopy theory. Modern Birkhäuser Classics. Birkhäuser Verlag, Basel, 2009. ISBN 978-3-0346-0188-7. Reprint of the 1999 edition [MR1711612]. doi:10.1007/978-3-0346-0189-4, MR:2840650. [1] [2] [3] [4] [5] [6] [7]
[Gor55] Russel A. Gordon. The integrals of Lebesgue, Denjoy, Perron, and Henstock. Volume 4 of Graduate Studies in Mathematics. American Mathematical Society, Providence, R.I, 1955. ISBN 0-8218-3805-9. [1] [2]
[Gou97] Fernando Q. Gouvêa. $p$-adic numbers. Second edition. Universitext. Springer-Verlag, Berlin, 1997. ISBN 3-540-62911-4. An introduction. doi:10.1007/978-3-642-59058-0, MR:1488696, URL: https://doi.org/10.1007/978-3-642-59058-0. [1] [2] [3] [4] [5]
[Gra83] R. L. Graham. Applications of the FKG Inequality and Its Relatives, pages 115–131. Springer Berlin Heidelberg, Berlin, Heidelberg, 1983. doi:10.1007/978-3-642-68874-4_6, URL: https://doi.org/10.1007/978-3-642-68874-4_6. [1] [2]
[Gra11] George Grätzer. Lattice Theory: Foundation. Springer, Basel, 2011. ISBN 978-3-0348-0018-1. doi:10.1007/978-3-0348-0018-1, MR:2768581. [1] [2]
[Gri69a] Pierre-Antoine Grillet. The Tensor Product of Commutative Semigroups. Transactions of the American Mathematical Society, 138:281–293, 1969. doi:10.1090/S0002-9947-1969-0237688-1. [1]
[Gri69b] Pierre-Antoine Grillet. The Tensor Product of Semigroups. Transactions of the American Mathematical Society, 138:267–280, 1969. doi:10.1090/S0002-9947-1969-0237687-X.
[Gri16] D. Grinberg. The Clifford algebra and the Chevalley map- a computational approach (summary version 1). Jun 2016. URL: http://mit.edu/~darij/www/algebra/chevalleys.pdf. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[Gro57] Alexander Grothendieck. Sur quelques points d'algèbre homologique. Tohoku Math. J. (2), 9:119–221, 1957. doi:10.2748/tmj/1178244839, MR:102537, URL: https://doi.org/10.2748/tmj/1178244839. [1]
[Gui80] René Guitart. Ann. Sci. Math. Québec, 4(2):103–125, 1980. MR:599050. [1]
[Gun92] Carl A. Gunter. Semantics of Programming Languages: Structures and Techniques. MIT Press, 1992. ISBN 0262570955. [1] [2] [3]
[GMM] Alena Gusakov, Bhavik Mehta, Kyle A. Miller. Formalizing Hall's Marriage Theorem in Lean. arXiv:2101.00127. [1]
[Hal35] P. Hall. On Representatives of Subsets. Journal of the London Mathematical Society, s1-10(1):26–30, Jan 1935. doi:10.1112/jlms/s1-10.37.26. [1]
[Hal50a] Paul R Halmos. Measure theory. Springer-Verlag New York, 1950. ISBN 978-1-4684-9440-2. doi:10.1007/978-1-4684-9440-2. [1] [2] [3]
[Hal50b] Paul R Halmos. Measure theory. Volume 18. Springer, 1950. ISBN 0-387-90088-8.
[Hal66] James D. Halpern. Bases in vector spaces and the axiom of choice. Proc. Amer. Math. Soc., 17:670–673, 1966. doi:10.2307/2035388, MR:194340. [1]
[HvD19] Jesse Michael Han, Floris van Doorn. A Formalization of Forcing and the Unprovability of the Continuum Hypothesis. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving (ITP 2019), volume 141 of Leibniz International Proceedings in Informatics (LIPIcs), 19:1–19:19. Dagstuhl, Germany, 2019. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. doi:10.4230/LIPIcs.ITP.2019.19, URL: http://drops.dagstuhl.de/opus/volltexte/2019/11074. [1] [2] [3] [4]
[HvD20] Jesse Michael Han, Floris van Doorn. A formal proof of the independence of the continuum hypothesis. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs. ACM, Jan 2020. doi:10.1145/3372885.3373826, URL: https://doi.org/10.1145/3372885.3373826. [1] [2] [3] [4]
[HOS84] Harald Hanche-Olsen, Erling Størmer. Jordan operator algebras. Volume 21. Pitman, Boston, MA, 1984. Zbl:0561.46031. [1] [2]
[HWHBS08] GH Hardy, EM Wright, Roger Heath-Brown, Joseph Silverman. An Introduction to the Theory of Numbers. Oxford University Press, 2008. [1] [2] [3]
[HWW93] Peter Harmand, Dirk Werner, Wend Werner. $M$-ideals in Banach spaces and Banach algebras. Volume 1547. Berlin: Springer-Verlag, 1993. ISBN 3-540-56814-X. doi:10.1007/BFb0084355, Zbl:0789.46011. [1]
[Har67] Robin Hartshorne. Local cohomology. Lecture Notes in Mathematics, No. 41. Springer-Verlag, Berlin-New York, 1967. A seminar given by A. Grothendieck, Harvard University, Fall, 1961. MR:0224620. [1]
[Har77] Robin Hartshorne. Algebraic geometry. Springer-Verlag, New York-Heidelberg, 1977. ISBN 0-387-90244-9. Graduate Texts in Mathematics, No. 52. MR:0463157. [1]
[Hat02] Allen Hatcher. Algebraic topology. Cambridge: Cambridge University Press, 2002. ISBN 0-521-79540-0. Zbl:1044.55001. [1]
[Haz09] Michiel Hazewinkel. Witt vectors. Part 1. Handbook of Algebra, pages 319–472, 2009. doi:10.1016/s1570-7954(08)00207-6, URL: http://dx.doi.org/10.1016/S1570-7954(08)00207-6. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
[Hig52] Graham Higman. Ordering by Divisibility in Abstract Algebras. Proceedings of the London Mathematical Society, s3-2(1):326-336, 1952. doi:10.1112/plms/s3-2.1.326. [1]
[HS00] Marc Hindry, Joseph H. Silverman. Diophantine geometry. Volume 201 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. An introduction. [1]
[Hoc] Mel Hochster. Local cohomology. URL: https://dept.math.lsa.umich.edu/~hochster/615W11/loc.pdf. [1]
[Hod97] Wilfrid Hodges. A Shorter Model Theory. Cambridge University Press, USA, 1997. ISBN 0521587131. [1]
[Hof79] Douglas R Hofstadter. Gödel, Escher, Bach: an eternal golden braid. Penguin books. Basic Books, New York, NY, 1979. [1]
[Hov01] Mark Hovey. Model category structures on chain complexes of sheaves. Trans. Amer. Math. Soc., 353(6):2441–2457, 2001. doi:10.1090/S0002-9947-01-02721-0, MR:1814077, URL: https://doi.org/10.1090/S0002-9947-01-02721-0. [1]
[How] Peter Howard. Second Order Elliptic PDE: The Lax-Milgram Theorem. URL: https://www.math.tamu.edu/~phoward/m612/s20/elliptic2.pdf. [1]
[Hua82] Loo-Keng Hua. Introduction to Number Theory. Springer, 1982. [1]
[HW91] John H. Hubbard, Beverly H. West. Differential Equations: A Dynamical Systems Approach. Volume 5. Springer, 1991. ISBN 978-1-4612-8693-6. doi:10.1007/978-1-4612-4192-8. [1]
[Hun02] Craig Huneke. The Friendship Theorem. The American Mathematical Monthly, 109(2):192–194, 2002. doi:10.1080/00029890.2002.11919853, URL: https://doi.org/10.1080/00029890.2002.11919853. [1]
[Joh02] Peter Johnstone. Sketches of an Elephant – A Topos Theory Compendium. Oxford University Press, 2002. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
[LS04] S. Lack, P. Sobociński. Adhesive categories. In Foundations of Software Science and Computation Structures, FoSSaCS '04, volume 2987 of LNCS, 273–288. Springer, 2004. URL: https://www.ioc.ee/~pawel/papers/adhesive.pdf. [1] [2]