Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T21:20:25.686Z Has data issue: false hasContentIssue false
  • English
  • Français

On Injective Sheaves

Published online by Cambridge University Press:  20 November 2018

H. Kleisli and
Y.C. Wu
H. Kleisli
Affiliation:
University of Ottawa
Y.C. Wu
Affiliation:
University of Ottawa
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A divisible abelian group D can be characterized by the following property: Every homomorphism from an abelian group A to D can be extended to every abelian group B containing A. This together with the result that every abelian group can be embedded in a divisible group is a crucial point in many investigations on abelian groups. It was Baer, [1], who extended this result to modules over an arbitrary ring, replacing divisible groups by injective modules, that is, modules with the property mentioned above. Another proof was found later by Eckmann and Schopf, [3]. This proof assumes the proposition to hold for abelian groups and transfers it in a very simple and elegant manner to modules. In the sequel, we shall refer to this proof as to the Eckmann-Schopf proof.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964, pp. 415 - 423
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Baer, R., Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), 800–806.Google Scholar
2. Cartan, H. and Eilenberg, S., Homological algebra, Princeton University Press, 1956.Google Scholar
3. Eckmann, B. und Schopf, A., Űber injective Moduln, Archiv der Math. 4 (1953), 75–78.Google Scholar
4. Godement, R., Topologie algébrique et théorie des faisceaux, Act. Sci. et Ind. 1252, Hermann Paris, 1958.Google Scholar
5. Gray, W.J., Sheaves with values in a category (Mimeographed, Columbia University).Google Scholar
6. Grothendieck, A., Sur quelques points d'algebre homologique, Tôhoku Math. J. 9 (1957), 119-221.Google Scholar
7. Heller, A. and Rowe, K. A., On the category of sheaves, Amer. J. Math. 84 (1962), 205–216.Google Scholar
8. Kan, D. M., Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294–329.Google Scholar
9. Maranda, J. M., Injective structures, Trans. Amer. Math. Soc. 110 (1964), 98–135.Google Scholar