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Duality in topological algebra

Published online by Cambridge University Press:  17 April 2009

B.J. Day
B.J. Day
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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Abstract

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Aspects of duality relating to compact totally disconnected universal algebras are considered. It is shown that if P is a ““basic“ set of injectives in a variety of compact totally disconnected algebras then the category P of P-copresentable objects is in duality with the class of all G-copresentable algebras on P, where G: P → Ens is the forgetful functor and an algebra is taken to mean a finite-product-preserving functor from P to Ens.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 3 , June 1978 , pp. 475 - 480
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Borceux, Francis and Day, Brian J., “Universal algebra in a closed category“ (Preprint, Univ. Cath. de Louvain, 1977).Google Scholar
[2]Choe, Tae Ho, “Zero-dimensional compact associative distributive universal algebras“, Proc. Amer. Math. Soc. 42 (1974), 607–613.CrossRefGoogle Scholar
[3]Choe, Tae Ho, “Injective and projective zero-dimensional compact universal algebras“, Algebra Universalis 7 (1977), 137–142.CrossRefGoogle Scholar
[4]Kelly, G.M., “Monomorphisms, epimorphisms, and pull-backs”, J. Austral. Math. Soc. 9 (1969), 124–142.CrossRefGoogle Scholar
[5]Lane, Saunders Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).CrossRefGoogle Scholar
[6]Schubert, Horst, Categories (translated by Gray, Eva. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar