Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-10T22:31:55.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Adams completion for cohomology theories arising from Kan extensions

Part of: Homotopy theory

Published online by Cambridge University Press:  09 April 2009

Sribatsa Nanda
Sribatsa Nanda
Affiliation:
Mathematics Department Regional Engineering CollegeRourkela 769008 (Orissa), India
Rights & Permissions [Opens in a new window]

Abstract

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.

It is shown that a cohomology theory over an admissible category, which is obtained from an additive cohomology theory over a smaller admissible category, through the Kan extension process, always admits global Adams completion.

MSC classification

Secondary: 55P60: Localization and completion
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 431 - 438
Copyright
Copyright © Australian Mathematical Society 1980

References

Adams, J. F. (1973), ‘Idempotent functors in homotopy theory’, Proc. Geometry Conference, Tokyo.Google Scholar
Deleanu, A. (1974), ‘Existence of the Adams completion for CW-complexes’, J. Pure Appl. Algebra 4, 299–308.CrossRefGoogle Scholar
Deleanu, A. (1975), ‘Existence of the Adams completion for objects of cocomplete categories’, J. Pure Appl. Algebra 6, 31–39.CrossRefGoogle Scholar
Deleanu, A., Frei, A. and Hilton, P. (1973), ‘Generalised Adams completion’, Cahiers Topologie Géom. Différetielle, XV-1, pp. 61–82.Google Scholar
Deleanu, A. and Hilton, P. (1968), ‘Some remarks on general cohomology theories’, Math. Scand. 22. 227–240.CrossRefGoogle Scholar
Deleanu, A. and Hilton, P. (1971), ‘On Kan extension of cohomology theories and Serre class of groups’, Fund. Math. 73, 143–165.CrossRefGoogle Scholar
Hilton, P. (1968), ‘On the construction of cohomology theories’, Rend. Mat. (6) 1, 1–14.Google Scholar
Nanda, S. (1979), ‘A note on the universe of a category of fractions’, Canad. Math. Bull., to appear.Google Scholar