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Goursat's Theorem and Homological Algebra

  • Joachim Lambek (a1)

Extract

This expository note consists of two parts: In the first we present a homological formulation of Goursat's theorem. In the second we indicate how some rudimentary concepts of homological algebra can be introduced with the help of this form of Goursat's theorem. The second part is addressed to those readers with an algebraic background who wish to be initiated into homological algebra as painlessly as possible. The ideas developed here are close to the spirit of [5, Chapter II, § 6], where further references may be found. In fact, these ideas are very much in the air, and any originality in the present note is purely coincidental.

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Copyright

References

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1. Bourbaki., N., Éléments de Mathématique XXVII, Paris 1961.
2. Cartan, H. and Eilenberg., S., Homological Algebra, Princeton 1956.
3. Goursat, É., Sur les substitutions orthogonales …, Ann. Sci. Éc. Norm. Sup. (3), 6(1889), 9102.
4. Lambek., J., Goursat's Theorem and the Zassenhaus Lemma, Can. J. Math. 10(1958), 4556.
5. MacLane., S., Homology, New York 1963.
6. Shoda., K., Allgemeine Algebra, Osaka Math. J. 2 (1949), 182225.
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Goursat's Theorem and Homological Algebra

  • Joachim Lambek (a1)

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