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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Singular homology as a derived functor


Author: G. S. Rinehart
Journal: Trans. Amer. Math. Soc. 174 (1972), 243-256
MSC: Primary 18E25; Secondary 55B10
DOI: https://doi.org/10.1090/S0002-9947-1972-0314937-2
MathSciNet review: 0314937
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Abstract: A general theory of relative derived tunctors is applied to the category of topological spaces to obtain singular homology and cohomology, verify the Eilenberg-Streenrod axioms, and show that singular and simplicial theory agree.


References [Enhancements On Off] (What's this?)

  • 1. M. Artin, Grothendieck topologies, Harvard University, Cambridge, Mass., 1962 (mimeographed notes).
  • [1] G. S. Rinehart, Note on the homology of a fiber product of groups, Proc. Amer. Math. Soc. 24 (1970), 548-552. MR 41 #1838. MR 0257184 (41:1838)
  • [2] G. S. Rinehart, Satellites and cohomology, J. Algebra 12 (1969), 295-329; Errata, ibid. 14 (1970), 125-126. MR 39 #6953; MR 40 #1455. MR 0245647 (39:6953)
  • [3] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0314937-2
Keywords: Singular homology as a derived functor, Eilenberg-Steenrod axioms, comparison of singular and simplicial homology
Article copyright: © Copyright 1972 American Mathematical Society

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