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Complete functors in homology I. Chain maps and endomorphisms

  • G. M. Kelly (a1)

There is a sense in which the homology group HA of a free Abelian chain complex A may be said to be a ‘complete system of invariants’ of A, to within chain equivalence; certainly any graded Abelian group G is isomorphic to HA for a suitable A, and if HA and HB are isomorphic then A and B are chain equivalent. Such a result is useful in showing that it is fruitless to seek other homotopy invariants of A; whatever depends only on the homotopy class of A depends only on HA, so that we can, for instance, predict the existence of a formula giving H(AG), to within isomorphism, in terms of HA and G. The theorem on the existence and uniqueness to within chain equivalence of projective resolutions of modules is a variant of the above theorem, more general in one direction and more special in another.

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(1)Kelly, G. M.On the radical of a category. J. Austral. Math. Soc. (to appear).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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