Book Review
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MathSciNet review:
1567186
Full text of review:
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Book Information:
Author:
Jan R. Strooker
Title:
Introduction to categories, homological algebra and sheaf cohomology
Additional book information:
Cambridge Univ. Press, Cambridge, Great Britain, 1978, ix + 246 PP.
Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
Samuel Eilenberg and Saunders MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294. MR 13131, DOI 10.1090/S0002-9947-1945-0013131-6
Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, N.J., 1952. MR 0050886
Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240
Nicolae Popesco and Pierre Gabriel, Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris 258 (1964), 4188–4190 (French). MR 166241
Roger Godement, Topologie algébrique et théorie des faisceaux, Publications de l’Institut de Mathématique de l’Université de Strasbourg, XIII, Hermann, Paris, 1973 (French). Troisième édition revue et corrigée. MR 0345092
Peter John Hilton and Urs Stammbach, A course in homological algebra, Graduate Texts in Mathematics, Vol. 4, Springer-Verlag, New York-Berlin, 1971. MR 0346025
Daniel M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294–329. MR 131451, DOI 10.1090/S0002-9947-1958-0131451-0
Joachim Lambek, Goursat’s theorem and homological algebra, Canad. Math. Bull. 7 (1964), 597–608. MR 174612, DOI 10.4153/CMB-1964-055-7
Joachim Lambek, Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Mathematics, Vol. 177, Springer-Verlag, Berlin-New York, 1971. With an appendix by H. H. Storrer on torsion theories and dominant dimensions. MR 0284459
J. Lambek and B. A. Rattray, A general Stone-Gel′fand duality, Trans. Amer. Math. Soc. 248 (1979), no. 1, 1–35. MR 521691, DOI 10.1090/S0002-9947-1979-0521691-4
Joachim Lambek, Goursat’s theorem and homological algebra, Canad. Math. Bull. 7 (1964), 597–608. MR 174612, DOI 10.4153/CMB-1964-055-7
Saunders MacLane, Homology, 1st ed., Die Grundlehren der mathematischen Wissenschaften, Band 114, Springer-Verlag, Berlin-New York, 1967. MR 0349792
Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872
Barry Mitchell, Theory of categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965. MR 0202787
N. Popescu, Abelian categories with applications to rings and modules, London Mathematical Society Monographs, No. 3, Academic Press, London-New York, 1973. MR 0340375
Dieter Puppe, Über die Axiome für abelsche Kategorien, Arch. Math. (Basel) 18 (1967), 217–222 (German). MR 222142, DOI 10.1007/BF01900624
Nobuo Yoneda, On the homology theory of modules, J. Fac. Sci. Univ. Tokyo Sect. I 7 (1954), 193–227. MR 68832
- 1.
- H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 0077480
- 2.
- S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294. MR 13131
- 3.
- S. Eilenberg and M. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, Princeton, N. J., 1952. MR 50886
- 4.
- P. Freyd, Abelian categories. Harper and Row, New York, 1964. MR 166240
- 5.
- P. Gabriel and N. Popescu, Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C. R. Acad. Sci. Paris, Sér. A 258 (1964), 4188-4191. MR 166241
- 6.
- R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1964. MR 345092
- 7.
- P. J. Hilton and U. Stammbach, A course in homological algebra, Springer-Verlag, Berlin and New York, 1971. MR 346025
- 8.
- D. M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329. MR 131451
- 9.
- J. Lambek, Goursat's theorem and homological algebra, Canad. Math. Bull. 7 (1964), 597-608. MR 174612
- 10.
- J. Lambek, Torsion theories, additive semantics and rings of quotients, Lecture Notes in Math., vol. 177, Springer-Verlag, Berlin and New York, 1971. MR 284459
- 11.
- J. Lambek and B. A. Rattray, A general Stone-Gelfand duality, Trans. Amer. Math. Soc. 248 (1979), 1-35. MR 521691
- 12.
- J. B. Leicht, Axiomatic proof of J. Lambek's homological theorem, Canad. Math. Bull. 7 (1964), 609-613. MR 174613
- 13.
- S. Mac Lane, Homology, Die Grundlehren der Mathematischen Wissenschaften, Band 114, Springer-Verlag, Berlin and New York, 1963. MR 349792
- 14.
- S. Mac Lane, Categories for the working mathematician, Springer-Verlag, Berlin and New York, 1971. MR 1712872
- 15.
- B. Mitchell, Theory of categories, Academic Press, New York, 1965. MR 202787
- 16.
- N. Popescu, Abelian categories with applications to rings and modules, Academic Press, London and New York, 1973. MR 340375
- 17.
- D. Puppe, Über die Axiome für abelsche Kategorien, Arch. Math. (Basel) 18 (1967), 217-222. MR 222142
- 18.
- N. Yoneda, On the homology of modules, J. Fac. Sci. Tokyo I 7 (1954), 193-227. MR 68832
Review Information:
Reviewer:
J. Lambek
Journal:
Bull. Amer. Math. Soc.
1 (1979), 919-928
DOI:
https://doi.org/10.1090/S0273-0979-1979-14693-7