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A Homology Theory for Small Categories

  • Charles E. Watts

Abstract

The notion of derived functors is well-established as being a powerful and profound tool in diverse areas of mathematics. The theme of Cartan-Eilenberg [1] is that almost all algebraic homology theories are examples thereof; and Grothendieck [5] displays Cech cohomology of topological spaces as a further deep application.

Keywords

Abelian Group Exact Sequence Direct Limit Small Category Homological Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Cartan, H., and S. Eilenberg: Homological algebra. Princeton: Princeton University Press 1956.MATHGoogle Scholar
  2. [2]
    Deheuvels, R.: Homologie des ensembles ordonnés et des espaces topologiques. Bull. Soc. Math. de France 90, 261–321 (1962).MathSciNetMATHGoogle Scholar
  3. [3]
    Eilenberg, S., and S. MacLane: On the groups H (π, n) I. Ann. Math. 58, 55–106 (1953).MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Godement, R.: Théorie des Faisceaux. Paris: Hermann et Cie. 1958.MATHGoogle Scholar
  5. [5]
    Grothendieck, A.: Sur quelques points d’algèbre homologique. Tohoku Math. J. 9, 119–221 (1957).MathSciNetMATHGoogle Scholar
  6. [6]
    Nöbeling, C.: Über die Derivierten des Inversen und des Direkten Limes einer Modulfamilie. Topology 1, 47–61 (1962).MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Watts, C.: Homological algebra of categories I (to appear).Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1966

Authors and Affiliations

  • Charles E. Watts
    • 1
  1. 1.Department of MathematicsThe University of RochesterRochesterUSA

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