41. Extending maps of plane Paano continua, Duke, vol 6(1940) pp 216-228 42. Extensions of homeomorphians on the sphere, Lectures in Topology, the University of Michigan, Conference of 1940, University of Michigan Press, 1941, pp 223-236

Papers on Topology and Algebra, written jointly with Prof. S. Eilenberg (University of Michigan and Indiana University)

43. Infinite cycles and homologies, Proceedings, NAS, vol 27(1941), pp 535-539 Group extensions and homology, Annals, Vol 43(1942) pp 757-831

44.

45.

46.

47.

Relations between homology and homotopy groups, Proceedings, NAS, vol 29 (1943) pp 155-158

Relations between homology and homotopy groups of spaces, Annals of Mathe-
matics, vol 46(1945) pp 480-507

Natural isomorphisms in group theory, Proceedings, MAS, vol 28(1942)
PP 537-543

48. General Theory of natural equivalence, Transactions, vol 58(1945) pp 231-294 49. Cohomology theory in abstract groups I, Annals of Mathematics, vol 48 (1947) pp 51-78

50. Cohomology theory in abstract groups II, Group extensions with a nonabelian kernel, Annals of Mathematics (1946) pp 326-341

51. Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proceedings, NAS, pp 277-280(1946)

52.

On Homology groups of infinite complexes and compacta, Appendix A in 8.
Lefschetz, Algebraic Topology (1942) pp 344-349

53. Algebraic cohomology and loops. Duke Math, J. v 14(1947) pp 435-463
54. Cohomology and Galois theory 1. Normality of algıbras and Teichmuller's
cocycle. Trans. AMS, v. 64(1948) pp 1-20

55. Symmetry of algebras over number fields. Bulletin AMS, v. 54(1948) PP 328-333

56. Groups, categories and duality. Proc. National Acad. Sci. USA. v. 34 (1948) pp 263-267

57.

Non-associative method for associative algebras, Bulletin AMS, v 54(1948)
PP 897-902

58. Homology of spaces with operators II. Transactions AMS, v. 65(1949) pp 49-99

59.

60.

61.

Cohomology theory in abstract groups III Operator homeomorphisms of kernels.
Ann. Math. v. 50(1949) pp 736-761

Relations between homology and homotopy groups of spaces II. Ann. Math.
v. 51(1930) pp 514-533

Cohomology theory of abelian groups and homotopy theory. Proc. NAS
(I, v. 36(1950) pp 443-447)

62. Cohomology theory of abelian groups and homotopy theory. Proc. NAS
(II, v. 36(1950) pp 657-663)

63. Cohomology theory of abelian groups. Proc. Inter. Congr. Math. ▼ 2(1950) Cambridge pp 8-14

64, Cohomology theory of abelian groups and homotopy theory III. Proc. Nat. Acad. Sci. USA. (1951) pp 307-310

65. Hamolegy theories for multiplicative systems. Trans. AMS. v. 71(September 1951) pp 294-330

66. Cohumology theories of abelian groups IV. Proc. Nat. Acad. Sci. USA v. 38 (1952) pp 325-329

67. Acyclic models. Amer. Jour. Nath. v. 75(January 1953) pp 189-199

68.

On the groups H( п, n) I. Ann. Math. v. 58(1953) pp 55-106

69.

70.

71.

On the groups H(π,n) II. Methods of computation. Ann. Math. v. 60(1954)
PP 49-139

On the groups H(IT,n) III. Operations and obstructions.
(1954) pp 513-557

Ann. Math. v. 60

Homology theory of abelian groups. Canadian J. Math. v. 7(January 1955)
PP 43-55

1. Other Joint Papers:

72. With J.B.C. Whitehead: On the 3-type of a complex. Proc. Nat. Acad. Sci. v. 36(January 1950) pp 41-48

J. Papers on Homological Algebra

73. Homology products in K(I,n). Proc. AMS. v. 5(August 1954) pp 642-651 74. Slide and torsion products for modules. Unive. Politec. Torino Pand. Sem. Mat. 15(1955-56) pp 281-309

75. Homologie des anneaux et des modules. Colloque de Topologie algebraique, Lourain 1956, pp 55-80

76.

77.

78.

Extensions and obstructions for rings. Ill. J. Math. vol. 2, No. 3(Sept.
1958) pp. 316-356

A proof of the subgroup theorem for free products. Mathematika 5(1958)
PP 13-19

Group extensions by primary abelian groups. Trans. Amer. Math. So. (April, 1963) vol. 95, No. 1, pp 1-16

L. Category Theory

79. Duality for groups. Bulletin AMS. v. 56(November 1950) pp 485-516 Locally small categories and the foundations of set theory. Proc. Symp. on Foundations Math (Warsaw 1959) pp 25-43

80.

81.

An algebra of additive relations. Proc. Natl. Acad. Scis. vol. 47 No. 7 (July 1961) pp 1043-1051

82. Natural associativity and commutativity. No. 4. Fall, 1963 pp 28-46

83.

84.

Rice University Studies, vol 49,

Categorical algebra. Bull. AMS (January 1965) v. 71, No. 1.

PP 40-106

Projective classes and acyclic models, with A. Deld and U. Oberst, Forthcom ing, Springer Lecture Notes

40-498 O-75-3

L.

84. Projective classes and acyclic models, with A. Dold and
U. Oberst, pp 78-91 in Reports of the Midwest Category
Seminar, Lecture Notes in Mathematies, vol. 47, Springer-
Verlag, New York, 1967.

85. Possible programs for categorista, pp 123-131 in Category
Theory, Homology Theory and Their Applications I, Lecture
Notes in Mathematies, vol. 86, Springer-Verlag, New York,
1968.

86. Foundations for Categories and Sets, pp. 146-164, in Cate-
gery Theary, Homology Theory and Their Applications II,
Lecture Notes in Mathematics, vol. 92, Springer-Verlag,
New York, 1969.

87. Foundations of Mathematics, Category Th ory, pp 286-294,
in Contemporary Philosophy A Survey, edited by Raymond
Klibansky, Florence, La Nuova, Italia Editrice.

88.

89.

90.

91.

92.

93.

Coherence and canonical maps, pp 231-242 in Symposia Mathe-
matica, vol. IV, Assoguidi, Bologna, 1970 (Conference held
March 25, 1969).

The influence of M. H. Stone on the origins of dategory, in
Functional Analysis and Related Fields, edited by Felix E.
Browder, Springer-Verlag, New York, 1970.

The Milgram Bar construction as a tensor produet of funetor,
pp 135-152, in The Steenrod Algebra and its Applications (A
Conference to selebrate N.E. Steenrod's sixtieth birthday)
Lecture Notes in Mathematics, vol. 168, Springer-Verlag,
New York, 1970.

Categorical algebra and set-theoretic foundations, in Axio-
matie Set Theory, Proceedings of Symposia in Pure Mathematics,
Vol. XIII, Part I, American Mathematical Society, Providence,
R. I. 1971.

(with G.M.Kelly) Goherence

Applied Algebra, voleringsteggio.

J. Pure and

(with G. N. Kelly) Closed scherence for a natural transformation, pp 1-28, in Coherence in Categories, Lecture Notes in Mathematies, Vol. 281, Springer-Verlag, New York, 1972.

94. One universe as a foundation for category theory, pp. 192-200, in Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics, Vol. 106, Springer-Verlag, 1969.

Mechanios

1.

Hamiltonian mechanics and geometry, American Math. Monthly,
Vol. 77, No. 6, June-July (1970), pp 570-586.

M.

N.

-6

2. Geometrical Mechanies, Parts I and II, Lecture Notes, University of Chicago, 1968.

Expositions and Books

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Corso de topologia general (Notas de Matematios) No. 11.
Translated by J.C. Valcares, Instituto de Nate. Para e Appli
de cons. Nat. de Pesquises, Rio de Janeiro, p 102 (1954).

Of course and courses, Amer. Math. Monthly, Vol. LXI, No. 3,
March 1954, pp. 151-157.

Algebra, Twenty-Third Year Book, Natl. Council of Teachers of
Math., 1957, pp. 100-144.

Metrie postulates for plane geometry, Amer. Math. Monthly, Vo`. 66, No. 7, August-September, 1959, pp. 543-555.

Some recent advances in algebra, MAA Studies in Modern Algebr
PP 9-34.

Some additional advances in algebra, MAA Studies in Modern
Algebra, pp 35-58.

Preliminary meeting on college level mathematics education,
Amer. Math. Monthly, vol. 72, No. 2, February, 1965, pp. 174-175.
Homology (422 pages), 1963, Springer-Verlag.

(with Garrett Birkhoff) A Survey of Modern Algebra, 1st edition
1941, 2nd edition 1953, 3rd edition 1965, Macmillan, New York.
(with Garrett Birkhoff) Algebra, 1967, Macmillan, New York.
Categories for the Working mathematician, Springer-Verlag,
New York, 1972.

Mappings as a Basic Mathematical Concept, pp 200-218, in Journeys in Science, Telfth AFOSH Science Seminar, edited by David . Arm, The Univaraity of Now Mexico, Albuquerque, 19. Science Policy

1.

2.

Leadership and quality in science, Basin Research and National Goals, Report to Committee on Science and Astronautics, U.S. House of Representatives, Natl. Acad. of Sciences, pp 189-202.

The future role of the federal government in mathematics, Amer,
Math. Monthly, vol. 74, No. 1, Part II (January, 1967) pp 92-300.

0. Bibliographical Memoirs

3. Gilbert Ames Bliss, Year Book of the American Philosophical Society for 1951, pp 288-291.

-7

2. Oswald Veblen, A biographical memoir, NAS (1964) pp 325-341.

3.

(with Jerome Hunsaker) Edwin Bidwell Wilson, A biographieal memoir, NAS (1973) pp 285-320.

July 1974