HOMOLOGY THEORIES FOR MULTIPLICATIVE SYSTEMS

@article{Eilenberg1951HOMOLOGYTF,
  title={HOMOLOGY THEORIES FOR MULTIPLICATIVE SYSTEMS},
  author={Samuel Eilenberg and Saunders Maclane},
  journal={Transactions of the American Mathematical Society},
  year={1951},
  volume={71},
  pages={294-330}
}
with d[x]=0. It is convenient to augment ^4°(II) by regarding the commutator quotient group 11/ [II, II] as the group of O-dimensional chains, with d[x]=x[n, TI]. The complex ^4°(I1) occurs in a topological problem in which IT plays the role of the fundamental group of a space. An analogous problem in which the fundamental group is replaced by a higher homotopy group has led us to believe that there exists for abelian groups a specific homology theory distinct from the one described above for… 
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New Proof for a Theorem of Eilenberg and Maclane
Here R is derived from any representation, G = F/R, with F a free group, and Hom(R, K) is the group of all homomorphisms of R into K. The group Hn+2(G, K) is defined in terms of an arbitrarily given
General theory of natural equivalences
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and
Cohomology theory of abelian groups and homotopy theory I.
  • S. Eilenberg, S. Maclane
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1950