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Epireflection operators vs perfect morphisms and closed classes of epimorphisms

Published online by Cambridge University Press:  17 April 2009

G.E. Strecker
G.E. Strecker
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania, USA
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Abstract

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Operators are defined that yield basic Galois closure operations for almost every category. These give rise to a new and more general approach for characterization of epireflective subcategories, and construction of epireflective hulls. As a by-product, satisfactory characterizations of classes of perfect morphisms and ω-extendable epimorphisms are obtained. Detailed proofs and examples will appear elsewhere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 359 - 366
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Harris, Douglas, “Katětov extension as a functor”, Math. Ann. 193 (1971), 171–175.CrossRefGoogle Scholar
[2]Herrlich, Horst, “A generalization of perfect maps”, General topology and its relations to modern analysis and algebra IV (Proceedings of the Third Prague Topological Symposium, 1971, to appear).Google Scholar
[3]Herrlich, Horst and Strecker, George E., “Coreflective subcategories”, Trans. Amer. Math. Soc. 157 (1971), 205–226.CrossRefGoogle Scholar
[4]Isbell, John R., “Structure of categories”, Bull. Amer. Math. Soc. 72 (1966), 619–655.CrossRefGoogle Scholar
[5]Kelly, G.M., “Monomorphisms, epimorphisms, and pull-backs”, J. Austral. Math. Soc. 9 (1969), 124–142.CrossRefGoogle Scholar