Abstract
We consider the extension of the notion of a projective module to that of a projective functor relative to a model set (as in Dold, MacLane, Oberst, 1967). Then taking projective resolutions of functors, we consider the usual associated homology.
We show that in some cases, including the classical simplicial homology of topological spaces, the model set can be replaced by a model set having only one element. We show that when the model set consists of a single element the homology modules can be interpreted as values of the Torsion functor. In the case of simplicial homology of topological spaces these Tors will be shown to be analogous to the Tors which occur in group homology.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
André, M.: Homologie des Algèbres Commutatives, Springer-Verlag, 1974.
Chapman, T. A.: Lectures on the Hilbert Cube, AMS, 1976.
Dold, A., MacLane, S. and Oberst, U.: Projective Classes and Acyclic Models, Lecture Notes in Math. 47, 1967.
Enochs, E. and Jenda, O. M. G.: Balanced functors applied to modules, J. Algebra 92 (1985), 303–310.
Enochs, E. and Jenda, O. M. G.: Gorenstein injective and projective modules, Math. Z. 220 (1995), 611–633.
Matlis, E.: Injective modules over noetherian rings, Pacific J. Math. 8 (1958), 511–528.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Branner, F.M., Enochs, E.E. Homology with Models and Tor. Applied Categorical Structures 5, 123–129 (1997). https://doi.org/10.1023/A:1008638301529
Issue Date:
DOI: https://doi.org/10.1023/A:1008638301529