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Cartan-Whitehead decomposition as Adams cocompletion

Part of: Operations and obstructions Homotopy theory General theory of categories and functors

Published online by Cambridge University Press:  09 April 2009

A. Behera  and
S. Nanda
A. Behera
Affiliation:
Mathematics Department University of TorontoToronto, Ontario M5S 1A1, Canada
S. Nanda
Affiliation:
Mathematics Department Regional Engineering College, Rourkela Rourkela, Orissa 769 008, India
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Abstract

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Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, the Adams cocompletion of an object in a category. In this paper the different stages of the Cartan-Whitehead decomposition of a 0-connected space are shown to be the cocompletions of the space with respect to suitable sets of morphisms.

MSC classification

Secondary: 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 55P60: Localization and completion 55S45: Postnikov systems, $k$-invariants
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 223 - 226
Copyright
Copyright © Australian Mathematical Society 1987

References

Deleanu, A., Frei, A. and Hilton, P. (1972), ‘Generalized Adams completion’, Cahiers de Topologie et Geornetrie Differentielle, XV-1, 61–82.Google Scholar
Eckmann, B. and Hilton, P. (1964), ‘Unions and intersections in homotopy theory’, Comm. Math. Helv. 38, 293–307.CrossRefGoogle Scholar
Nanda, S. (1979), ‘Adams completion and its applications’, Queen's Papers in Pure and Applied Mathematics, No. 51, Queen's University, Kingston, Ontario, Canada.Google Scholar
Nanda, S. (1980), ‘A note on the universe of a category of fractions’, Canad. Math. Bull. 23 (4), 425–427.CrossRefGoogle Scholar