A Homology Theory for Small Categories

  • Charles E. Watts


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.


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  1. [1]
    Cartan, H., and S. Eilenberg: Homological algebra. Princeton: Princeton University Press 1956.MATHGoogle Scholar
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    Deheuvels, R.: Homologie des ensembles ordonnés et des espaces topologiques. Bull. Soc. Math. de France 90, 261–321 (1962).MathSciNetMATHGoogle Scholar
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    Eilenberg, S., and S. MacLane: On the groups H (π, n) I. Ann. Math. 58, 55–106 (1953).MathSciNetMATHCrossRefGoogle Scholar
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    Godement, R.: Théorie des Faisceaux. Paris: Hermann et Cie. 1958.MATHGoogle Scholar
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    Grothendieck, A.: Sur quelques points d’algèbre homologique. Tohoku Math. J. 9, 119–221 (1957).MathSciNetMATHGoogle Scholar
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    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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