Topology and logic as a source of algebra

1. Richard F. Arens, Operations induced in conjugate spaces, Proc. Internat. Congr. of Math. (Cambridge, Mass., 1950), vol. I, Amer. Math. Soc., Providence, R.I., 1952, pp. 532-533.

2. Richard F. Arens, The adjoint of a bilinear operator, Proc. Amer. Math. Soc. 2 (1951), 839-848. MR 13, 659.

Zentralblatt MATH: 0044.32601

Mathematical Reviews (MathSciNet): MR45941

Digital Object Identifier: doi:10.1090/S0002-9939-1951-0045941-1

3. Richard F. Arens, Operations induced in function classes, Monatsh. Math. 55 (1951), 1-19. MR 13, 372.

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Digital Object Identifier: doi:10.1007/BF01300644

4. M. Artin, A. Grothendieck and J. L. Verdier, La théorie des topos et cohomologie étale des schémas (SGA 4), vols. I, II, III, (Séminaire de géométrie algébrique du Bois-Marie 1963/64), Lecture Notes in Math., vols. 269, 270, 305, Springer-Verlag, Berlin, Heidelberg and New York, 1972, 1973.

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5. R. Baer, Erweiterung von Gruppen und ihren Isomorphismen, Math. Z. 38 (1934), 375-416.

Mathematical Reviews (MathSciNet): MR1545456

Digital Object Identifier: doi:10.1007/BF01170643

6. Michael Barr, Cohomology and obstructions: Commutative algebras, Seminar on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Lecture Notes in Math., vol. 80, Springer-Verlag, Berlin, Heidelberg and New York, 1969, pp. 357-373. MR 42 #6075.

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Mathematical Reviews (MathSciNet): MR271192

7. H. Bass, Algebraic K-theory, Benjamin, New York and Amsterdam, 1968. MR 40 #2736.

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Mathematical Reviews (MathSciNet): MR249491

8. N. Bourbaki, Éléments de mathématique. XL Part I: Les structures fondamentales de l'analyse. Livre II: Algèbre, Chap. 5: Corps commutatifs, Actualités Sci. Indust., no. 1102, Hermann, Paris, 1950. MR 12, 6.

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Mathematical Reviews (MathSciNet): MR35759

9. H. Cartan, Séminaire Henri Cartan de l'École Normale Supérieure, 1954/1955, Algèbres d'Eilenberg-Mac Lane et homotopie, Secrétariat mathématique, Paris, 1955. MR 19, 438.

Zentralblatt MATH: 0116.24401

10. H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. MR 17, 1040.

Zentralblatt MATH: 0075.24305

Mathematical Reviews (MathSciNet): MR77480

11. E. Čech, Les groupes de Betti d'un complex infinie, Fund. Math. 25 (1935), 33-44.

12. G. J. Decker, The integral homology algebra of an Eilenberg-Mac Lane space, Thesis, Univ. of Chicago, Chicago, 1974.

Mathematical Reviews (MathSciNet): MR2611718

13. J. Duskin, K(Π,n)-torsors and the interpretation of "triple" cohomology, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2554-2557. MR 49 #5139.

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Mathematical Reviews (MathSciNet): MR340384

Digital Object Identifier: doi:10.1073/pnas.71.6.2554

14. J. Duskin, Simplicial methods and the interpretation of "triple" cohomology, Mem. Amer. Math. Soc. No. 163 (to appear).

Zentralblatt MATH: 0376.18011

Mathematical Reviews (MathSciNet): MR393196

15. E. Dyer and R. K. Lashof, Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35-88. MR 25 #4523.

Zentralblatt MATH: 0119.18206

Mathematical Reviews (MathSciNet): MR141112

Digital Object Identifier: doi:10.2307/2372804

16. B. Eckmann, Der Cohomologie-Ring einer beliebigen Gruppe, Comment. Math. Helv. 18 (1946), 232-282. MR 8, 166.

Zentralblatt MATH: 0061.40705

Mathematical Reviews (MathSciNet): MR17536

Digital Object Identifier: doi:10.1007/BF02568113

17. S. Eilenberg, Singular homology theory, Ann. of Math. (2) 45 (1944), 407-447. MR 6, 96.

Zentralblatt MATH: 0061.40603

Mathematical Reviews (MathSciNet): MR10970

Digital Object Identifier: doi:10.2307/1969185

18. S. Eilenberg, Automata, languages, and machines. Vol. A, Academic Press, New York, 1974.

Zentralblatt MATH: 0317.94045

Mathematical Reviews (MathSciNet): MR530382

19. S. Eilenberg and G. M. Kelly, A generalization of the functorial calculus, J. Algebra 3 (1966), 366-375. MR 32 #7618.

Zentralblatt MATH: 0146.02501

Mathematical Reviews (MathSciNet): MR190204

Digital Object Identifier: doi:10.1016/0021-8693(66)90006-8

20. S. Eilenberg and S. Mac Lane, Group extensions and homology, Ann. of Math. (2) 43 (1942), 757-831. MR 4, 88.

Zentralblatt MATH: 0061.40602

21. S. Eilenberg and S. Mac Lane, Natural isomorphisms in group theory, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 537-543. MR 4, 134.

Zentralblatt MATH: 0061.09203

Mathematical Reviews (MathSciNet): MR7421

Digital Object Identifier: doi:10.1073/pnas.28.12.537

22. S. Eilenberg and S. Mac Lane, Relations between homology and homotopy groups, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 155-158. MR 4, 224.

Zentralblatt MATH: 0061.40701

Mathematical Reviews (MathSciNet): MR7982

Digital Object Identifier: doi:10.1073/pnas.29.5.155

23. S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294. MR 7, 109.

Zentralblatt MATH: 0061.09204

Mathematical Reviews (MathSciNet): MR13131

24. S. Eilenberg and S. Mac Lane, Relations between homology and homotopy groups of spaces, Ann. of Math. (2) 46 (1945), 480-509. MR 7, 137.

Zentralblatt MATH: 0061.40702

Mathematical Reviews (MathSciNet): MR13312

Digital Object Identifier: doi:10.2307/1969165

25. S. Eilenberg and S. Mac Lane, Homology of spaces with operators. II, Trans. Amer. Math. Soc. 65 (1949), 49-99. MR 11, 379.

Zentralblatt MATH: 0034.11101

26. S. Eilenberg and S. Mac Lane, Relations between homology and homotopy groups of spaces. II, Ann. of Math. (2) 51 (1950), 514-533. MR 11, 735.

Zentralblatt MATH: 0036.12602

Mathematical Reviews (MathSciNet): MR35435

Digital Object Identifier: doi:10.2307/1969365

27. S. Eilenberg and S. Mac Lane, Acyclic models, Amer. J. Math. 75 (1953), 189-199. MR 14, 670.

Zentralblatt MATH: 0050.17205

28. S. Eilenberg and S. Mac Lane, On the groups H(Π,n). I, Ann. of Math. (2) 58 (1953), 55-106. MR 15, 54.

Zentralblatt MATH: 0050.39304

Mathematical Reviews (MathSciNet): MR56295

Digital Object Identifier: doi:10.2307/1969820

29. S. Eilenberg and S. Mac Lane, On the groups H(Π,n). II. Methods of computation, Ann. of Math. (2) 60 (1954), 49-139. MR 16, 391.

Zentralblatt MATH: 0055.41704

Mathematical Reviews (MathSciNet): MR65162

Digital Object Identifier: doi:10.2307/1969702

30. S. Eilenberg and S. Mac Lane, On the groups H(Π,n). III. Operations and obstructions, Ann. of Math. (2) 60 (1954), 513-557. MR 16, 392.

Zentralblatt MATH: 0057.15302

Mathematical Reviews (MathSciNet): MR65162

Digital Object Identifier: doi:10.2307/1969702

31. S. Eilenberg and J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. (2) 51 (1950), 499-513. MR 11, 734.

Zentralblatt MATH: 0036.12601

Mathematical Reviews (MathSciNet): MR35434

Digital Object Identifier: doi:10.2307/1969364

32. C. Elgot, Monadic computation and iterative algebraic theories, Proc. Logic Colloquium (Bristol, 1973) edited by H. E. Rose and J. C. Shepherdson, North-Holland Publishing Co., Amsterdam. Oxford 1975, pp. 175-230.

Zentralblatt MATH: 0327.02040

Mathematical Reviews (MathSciNet): MR413584

33. D. B. A. Epstein, Functors between tensored categories, Invent. Math. 1 (1966), 221-228. MR 35 #4276.

Zentralblatt MATH: 0146.02502

Mathematical Reviews (MathSciNet): MR213412

Digital Object Identifier: doi:10.1007/BF01452242

33a. H. Freudenthal, Der Einfluss der Fundamentalgruppe auf die Bettischen Gruppen, Ann. of Math. (2) 47 (1946), 274-316. MR 8, 166.

Zentralblatt MATH: 0061.40706

Mathematical Reviews (MathSciNet): MR17535

Digital Object Identifier: doi:10.2307/1969247

34. P. Freyd, Abelian categories. An introduction to the theory of functors, Harper's Ser. in Modern Math., Harper & Row, New York, 1964. MR 29 #3517.

Zentralblatt MATH: 0121.02103

Mathematical Reviews (MathSciNet): MR166240

35. P. Freyd, Aspects of topoi, Bull. Austral. Math. Soc. 7 (1972), 1-76.

Zentralblatt MATH: 0252.18001

Mathematical Reviews (MathSciNet): MR396714

Digital Object Identifier: doi:10.1017/S0004972700044828

36. P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag, Berlin, Heidelberg and New York, 1967. MR 35 #1019.

Zentralblatt MATH: 0186.56802

Mathematical Reviews (MathSciNet): MR210125

37. G. Gentzen, Untersuchungen über das logische Schliessen. I, II, Math. Z. 39 (1934), 176-210, 405-431.

Mathematical Reviews (MathSciNet): MR1545497

Digital Object Identifier: doi:10.1007/BF01201353

38. M. Gerstenhaber, On the deformation of rings and algebras. II, Ann. of Math. (2) 84 (1966), 1-19. MR 34 #7608.

Zentralblatt MATH: 0147.28903

Mathematical Reviews (MathSciNet): MR207793

Digital Object Identifier: doi:10.2307/1970528

39. S. J. Goldberg, Extension of Lie algebras and the third cohomology group, Canad. J. Math. 5 (1953), 470-476. MR 15, 282.

Zentralblatt MATH: 0051.02303

Mathematical Reviews (MathSciNet): MR57853

Digital Object Identifier: doi:10.4153/CJM-1953-054-8

40. M. Hakim, Topos annelés et schémas relatifs, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 64, Springer-Verlag, Berlin and New York, 1972.

Zentralblatt MATH: 0246.14004

Mathematical Reviews (MathSciNet): MR364245

41. R. Hamsher, Eilenberg-Mac Lane algebras and their computation, Thesis, Univ. of Chicago, Chicago, Ill., 1973.

42. G. Hochschild, Cohomology classes of finite type and finite dimensional kernels for Lie algebras, Amer. J. Math. 76 (1954), 763-778. MR 16, 443.

Zentralblatt MATH: 0057.27204

Mathematical Reviews (MathSciNet): MR65547

Digital Object Identifier: doi:10.2307/2372650

43. G. Hochschild, Lie algebra kernels and cohomology, Amer. J. Math. 76 (1954), 698-716. MR 16, 109.

Zentralblatt MATH: 0055.26601

Mathematical Reviews (MathSciNet): MR63362

Digital Object Identifier: doi:10.2307/2372712

44. H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257-309. MR 3, 316.

Zentralblatt MATH: 0027.09503

Mathematical Reviews (MathSciNet): MR6510

Digital Object Identifier: doi:10.1007/BF02565622

45. H. Hopf, Relations between the fundamental group and the second Betti group, Lectures in Topology, Univ. of Michigan Press, Ann Arbor, Mich., 1941, pp. 315-316. MR 3, 135.

Zentralblatt MATH: 0063.02066

Mathematical Reviews (MathSciNet): MR5315

46. H. Hopf, Nachtrag zu der Arbeit Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 15 (1943), 27-32. MR 4, 173.

Zentralblatt MATH: 0027.09504

Mathematical Reviews (MathSciNet): MR7646

Digital Object Identifier: doi:10.1007/BF02565629

47. H. Hopf, Über die Bettischen Gruppen, die zu einer beliebigen Gruppe gehören, Comment. Math. Helv. 17 (1945), 39-79, MR 6, 279.

Zentralblatt MATH: 0061.40703

Mathematical Reviews (MathSciNet): MR12229

Digital Object Identifier: doi:10.1007/BF02566234

48. D. M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329. MR 24 #A1301.

Zentralblatt MATH: 0090.38906

Mathematical Reviews (MathSciNet): MR131451

Digital Object Identifier: doi:10.1090/S0002-9947-1958-0131451-0

49. D. M. Kan, A combinatorial definition of homotopy groups, Ann. of Math. (2) 67 (1958), 282-312. MR 22 #1897.

Zentralblatt MATH: 0091.36901

Mathematical Reviews (MathSciNet): MR111032

Digital Object Identifier: doi:10.2307/1970006

50. G. M. Kelly, On Mac Lane's conditions for coherence of natural associativities, commutativities, etc., J. Algebra 1 (1964), 397-402. MR 32 #132.

Zentralblatt MATH: 0246.18008

Mathematical Reviews (MathSciNet): MR182649

Digital Object Identifier: doi:10.1016/0021-8693(64)90018-3

51. G. M. Kelly and S. Mac Lane, Coherence in closed categories, J. Pure Appl. Algebra 1 (1971), no. 1, 97-140; erratum, ibid. no. 2, 219. MR 44 #278; 45 #1988.

Zentralblatt MATH: 0215.09703

Mathematical Reviews (MathSciNet): MR283045

Digital Object Identifier: doi:10.1016/0022-4049(71)90013-2

52. G. M. Kelly and S. Mac Lane, Closed coherence for a natural transformation, Coherence in Categories, Lecture Notes in Math., vol. 281, Springer-Verlag, Berlin, Heidelberg and New York, 1972, pp. 1-28. MR 48 #8591.

Zentralblatt MATH: 0245.18003

Mathematical Reviews (MathSciNet): MR374237

Digital Object Identifier: doi:10.1007/BFb0059554

53. A. Kock and G. C. Wraith, Elementary toposes, Lecture Notes Series, no. 30, Aarhus Universitet, Aarhus, Denmark, 1971.

Zentralblatt MATH: 0251.18015

Mathematical Reviews (MathSciNet): MR342578

54. J. Lambek, Deductive systems and categories. I. Syntactic calculus and residuated categories, Math. Systems Theory 2 (1968), 287-318. MR 38 #4277.

Zentralblatt MATH: 0176.28901

Mathematical Reviews (MathSciNet): MR235979

Digital Object Identifier: doi:10.1007/BF01703261

55. J. Lambek, Deductive systems and categories. II. Standard constructions and closed categories, Category Theory, Homology Theory and their Applications, I (Battelle Institute Conf., Seattle, Wash., 1968, Vol. One), Lecture Notes in Math., vol. 86, Springer-Verlag, Berlin, Heidelberg and New York, 1969, pp. 76-122. MR 39 #3967.

Zentralblatt MATH: 0198.33701

Mathematical Reviews (MathSciNet): MR242637

56. K. Lamotke, Semisimpliziale algebraische Topologie, Die Grundlehren der math. Wissenschaften, Band 147, Springer-Verlag, Berlin, Heidelberg and New York, 1968. MR 39 #6318.

Zentralblatt MATH: 0188.28301

Mathematical Reviews (MathSciNet): MR245005

57. F. W. Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-872. MR 28 #2143.

Zentralblatt MATH: 0119.25901

Mathematical Reviews (MathSciNet): MR158921

Digital Object Identifier: doi:10.1073/pnas.50.5.869

58. F. W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1506-1511. MR 30 #3025.

Zentralblatt MATH: 0141.00603

Mathematical Reviews (MathSciNet): MR172807

Digital Object Identifier: doi:10.1073/pnas.52.6.1506

59. F. W. Lawvere. (editor), Toposes, algebraic geometry and logic, Lecture Notes in Math., vol. 274, Springer-Verlag, Berlin, Heidelberg and New York, 1972. MR 48 #8592.

Zentralblatt MATH: 0233.00005

Mathematical Reviews (MathSciNet): MR376798

60. S. Mac Lane, Some interpretations of abstract linear dependence in terms of projective geometry, Amer. J. Math. 58 (1936), 236-240.

Mathematical Reviews (MathSciNet): MR1507146

Digital Object Identifier: doi:10.2307/2371070

61. S. Mac Lane, A lattice formulation for transcendence degrees and p-bases, Duke Math. J. 4 (1938), 455-468.

Mathematical Reviews (MathSciNet): MR1546067

Digital Object Identifier: doi:10.1215/S0012-7094-38-00438-7

Project Euclid: euclid.dmj/1077490785

62. S. Mac Lane, The uniqueness of the power series representation of certain fields with valuations, Ann. of Math. 39 (1938), 370-382.

Mathematical Reviews (MathSciNet): MR1503414

Digital Object Identifier: doi:10.2307/1968793

63. S. Mac Lane, Modular fields, I. Separating transcendence bases, Duke Math. J. 5 (1939), 372-393.

Mathematical Reviews (MathSciNet): MR1546131

Digital Object Identifier: doi:10.1215/S0012-7094-39-00532-6

Project Euclid: euclid.dmj/1077491235

64. S. Mac Lane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23-45. MR 1, 3.

Mathematical Reviews (MathSciNet): MR17

Digital Object Identifier: doi:10.1090/S0002-9947-1939-0000017-3

65. S. Mac Lane, Subfields and automorphism groups of p-adic fields, Ann. of Math. 40 (1939), 423-442.

Zentralblatt MATH: 0021.00501

Mathematical Reviews (MathSciNet): MR1503470

Digital Object Identifier: doi:10.2307/1968931

66. S. Mac Lane, Note on the relative structure of p-adic fields, Ann. of Math. (2) 41 (1940), 751-753. MR 2, 123.

Zentralblatt MATH: 0025.10404

Mathematical Reviews (MathSciNet): MR2860

Digital Object Identifier: doi:10.2307/1968854

67. S. Mac Lane, Modular fields, Amer. Math. Monthly 47 (1940), 259-274. MR 1, 328.

Mathematical Reviews (MathSciNet): MR1969

Digital Object Identifier: doi:10.2307/2302685

68. S. Mac Lane, Homology products in K(Π,n), Proc. Amer. Math. Soc. 5 (1954), 642-651. MR 16, 160.

Zentralblatt MATH: 0059.16405

Mathematical Reviews (MathSciNet): MR63674

69. S. Mac Lane, Extensions and obstructions for rings, Illinois J. Math. 2 (1958), 316-345. MR 20 #5228.

Zentralblatt MATH: 0081.03303

Mathematical Reviews (MathSciNet): MR98773

Project Euclid: euclid.ijm/1255454537

70. S. Mac Lane, Locally small categories and the foundations of set theory, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; PWN, Warsaw, 1961, pp. 25-43. MR 33 #168.

Zentralblatt MATH: 0116.00902

Mathematical Reviews (MathSciNet): MR191941

71. S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York: Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963; 3rd corrected printing, 1975. MR 28 #122.

Zentralblatt MATH: 0328.18009

Mathematical Reviews (MathSciNet): MR156879

72. S. Mac Lane, Some additional advances in algebra, Studies in Modern Algebra (A. A. Albert, editor), Studies in Math., vol. 2, The Math. Assoc, of Amer.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1963, pp. 35-58. MR 26 #3750.

Zentralblatt MATH: 0199.04803

Mathematical Reviews (MathSciNet): MR146228

73. S. Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28-46. MR 30 #1160.

Zentralblatt MATH: 0244.18008

Mathematical Reviews (MathSciNet): MR170925

74. S. Mac Lane, The influence of M. H. Stone on the origins of category theory, Functional Analysis and Related Fields (F. E. Browder, editor), Springer-Verlag, Berlin, Heidelberg and New York, 1970, pp. 228-241.

Zentralblatt MATH: 0261.18001

Mathematical Reviews (MathSciNet): MR263888

75. S. Mac Lane, The Milgram bar construction as a tensor product of functors, The Steenrod Algebra and its Applications (Proc. Conf. to Celebrate N. E. Steenrod's Sixtieth Birthday, Battelle Memorial Inst., Columbus, Ohio, 1970), Lecture Notes in Math., vol. 168, Springer-Verlag, Berlin, Heidelberg and New York, 1970; pp. 135-152. MR 42 #8495.

Zentralblatt MATH: 0216.45405

Mathematical Reviews (MathSciNet): MR273618

76. S. Mac Lane, Categories for the working mathematician, Springer-Verlag, Berlin, Heidelberg and New York, 1971.

Zentralblatt MATH: 0232.18001

Mathematical Reviews (MathSciNet): MR354798

77. S. Mac Lane, Sets, topoi, and internal logic in categories, Proc. Logic Colloquium (Bristol, 1973) edited by H. E. Rose and J. C. Shepherdson, North-Holland Publishing Co., Amsterdam. Oxford 1975, pp. 119-134.

Zentralblatt MATH: 0313.18001

Mathematical Reviews (MathSciNet): MR384545

78. S. Mac Lane and O. F. G. Schilling, Normal algebraic number fields, Trans. Amer. Math. Soc. 50 (1941), 295-384. MR 3, 102.

Mathematical Reviews (MathSciNet): MR5108

Digital Object Identifier: doi:10.1090/S0002-9947-1941-0005108-8

79. S. Mac Lane and F. K. Schmidt, The generation of inseparable fields, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 583-587. MR 3, 263.

Zentralblatt MATH: 0063.06800

Mathematical Reviews (MathSciNet): MR6153

Digital Object Identifier: doi:10.1073/pnas.27.12.583

80. E. Manes, Algebraic theories, Graduate Texts in Math., Springer-Verlag, Berlin, Heidelberg and New York (to appear).

Zentralblatt MATH: 0353.18007

Mathematical Reviews (MathSciNet): MR419557

81. J. P. May, Simplicial objects in algebraic topology, Van Nostrand Math. Studies, no. 11, Van Nostrand, Princeton, N.J., 1967. MR 36 #5942.

Zentralblatt MATH: 0165.26004

Mathematical Reviews (MathSciNet): MR222892

82. R. J. Milgram, The bar construction and abelian H-spaces, Illinois J. Math. 11 (1967), 242-250. MR 34 #8404.

Zentralblatt MATH: 0152.40502

Mathematical Reviews (MathSciNet): MR208595

Project Euclid: euclid.ijm/1256054662

83. M. Mori, On the three-dimensional cohomology group of Lie algebras, J. Math. Soc. Japan 5 (1953), 171-183. MR 15, 282.

Zentralblatt MATH: 0051.02304

Mathematical Reviews (MathSciNet): MR57854

Digital Object Identifier: doi:10.2969/jmsj/00520171

Project Euclid: euclid.jmsj/1261415546

84. D. G. Quillen, Homotopical algebra, Lecture Notes in Math, vol 43, Springer-Verlag, Berlin, Heidelberg and New York, 1967. MR 36 #6480.

Zentralblatt MATH: 0168.20903

Mathematical Reviews (MathSciNet): MR223432

85. D. G. Quillen, On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552-586. MR 47 #3565.

Zentralblatt MATH: 0249.18022

Mathematical Reviews (MathSciNet): MR315016

Digital Object Identifier: doi:10.2307/1970825

86. N. Saavedra Rivano, Catégories tannakiennes, Lecture Notes in Math., vol. 265, Springer-Verlag, Berlin, Heidelberg and New York, 1972. MR 49 #2769.

Zentralblatt MATH: 0241.14008

Mathematical Reviews (MathSciNet): MR338002

87. M. Rothenberg and N. E. Steenrod, The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc. 71 (1965), 872-875. MR 34 #8405.

Zentralblatt MATH: 0132.19201

Mathematical Reviews (MathSciNet): MR208596

Digital Object Identifier: doi:10.1090/S0002-9904-1965-11420-3

Project Euclid: euclid.bams/1183527356

88. J.-P. Serre, Cohomologie galoisienne, Cours au Collège de France, 1962-1963, 2nd. ed., Lectures Notes in Math., vol. 5, Springer-Verlag, Berlin, Heidelberg and New York, 1964. MR 31 #4785.

Zentralblatt MATH: 0136.02801

Mathematical Reviews (MathSciNet): MR180551

89. U. Shukla, Cohomologie des algèbres associatives, Ann. Sci. École Norm. Sup. (3) 78 (1961), 163-209. MR 24 #A2605.

Zentralblatt MATH: 0228.18005

Mathematical Reviews (MathSciNet): MR132769

90. J. D. Stasheff, Homotopy associativity of H-spaces. I, Trans. Amer. Math. Soc. 108 (1963), 275-292. MR 28 #1623.

Zentralblatt MATH: 0114.39402

Mathematical Reviews (MathSciNet): MR158400

91. N. E. Steenrod, Milgram's classifying space of a topological group, Topology 7 (1968), 349-368. MR 38 # 1675.

Zentralblatt MATH: 0177.51601

Mathematical Reviews (MathSciNet): MR233353

Digital Object Identifier: doi:10.1016/0040-9383(68)90012-8

92. D. P. Sullivan, Geometric topology, part 1, Localization, periodicity, and Galois symmetry, Mimeographed notes, M.I.T., Cambridge, Mass., 1970.

Zentralblatt MATH: 1078.55001

93. J. Tate, The higher dimensional cohomology groups of class field theory, Ann. of Math (2) 56 (1952), 294-297. MR 14, 252.

Zentralblatt MATH: 0047.03703

Mathematical Reviews (MathSciNet): MR49950

Digital Object Identifier: doi:10.2307/1969801

94. O. Teichmüller, p-Algebren, Deutsche Math. 1 (1936), 362-388.

95. O. Teichmüller, Diskret bewertete perfekte Körper mit unvollkommenem Restklassenkörper, J. Reine Angew Math. 176 (1936), 141-152.

96. O. Teichmüller, Über die sogenannte nichtkommutative Galoissche Theorie und die Relation $\xi\sb {łambda,µ,\nu}\xi\sb {łambda,µ\nu,\pi}\xi\sp {łambda}\sb {µ,\nu,\pi}=\xi\sb {łambda,µ,\nu \pi}\xi\sb {łambda,µ,\nu,\pi}$, Deutsche Math. 5 (1940), 138-149. MR 2, 122.

Mathematical Reviews (MathSciNet): MR2858

97. O. Veblen, Analysis situs, 2nd ed., Amer. Math. Soc. Colloq. Publ., vol. 5, part II, Amer. Math. Soc., Providence, R. I., 1931.

98. R. Voreadou, A coherence theorem for closed categories (to appear).

Mathematical Reviews (MathSciNet): MR622637

99. R. Voreadou, Non-commutative diagrams in closed categories (to appear).

100. A. Weil, Foundations of algebraic geometry, Amer. Math. Soc. Colloq. Publ., vol. 29, Amer. Math. Soc., Providence, R. I., 1946. MR 9, 303.

Zentralblatt MATH: 0063.08198

Mathematical Reviews (MathSciNet): MR23093

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Zentralblatt MATH: 0037.26101

Mathematical Reviews (MathSciNet): MR35997

Digital Object Identifier: doi:10.2307/1969511

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Mathematical Reviews (MathSciNet): MR1507091

Digital Object Identifier: doi:10.2307/2371182

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Mathematical Reviews (MathSciNet): MR1545972

Digital Object Identifier: doi:10.1215/S0012-7094-37-00306-5

Project Euclid: euclid.dmj/1077489917

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Mathematical Reviews (MathSciNet): MR1546071

Digital Object Identifier: doi:10.1215/S0012-7094-38-00442-9

Project Euclid: euclid.dmj/1077490789

Topology and logic as a source of algebra

References

Bulletin of the American Mathematical Society