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Characterizations of MacNeille completions and topological functors

Published online by Cambridge University Press:  17 April 2009

Hans-E. Porst
Hans-E. Porst
Affiliation:
Fachsektion Mathematik, Universität Bremen, Bremen, Germany.
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Abstract

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In this note we give external characterizations of absolutely topologicai functors U: A →X (where A may be a large category) as functors which are injective with respect to all functors based on the category X, or equivalently, which do not admit essential extensions over X. From this we deduce several characterizations and properties of the MacNeille completion of faithful functors. These results generalize the work of Horst Herriich [Math. Z. 150 (1976), 101–110] in case of small categories, where the crucial point of this generalization lies in the fact that we cannot make use of the existence of MacNeille completions and we therefore have to introduce a local-initial-completion-construction.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 2 , April 1978 , pp. 201 - 210
Copyright
Copyright © Australian Mathematical Society 1978

References

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