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Cogeneration of algebras in regular categories

Published online by Cambridge University Press:  17 April 2009

Jiří Adámek
Jiří Adámek
Affiliation:
Faculty of Electrical Engineering, České Vysoké Učení Technické v Praze, Czechoslovakia.
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Abstract

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A quotient algebra of a given algebra is said to be cogenerated by a quotient object if it is contained in the quotient object and is the biggest with this property. Triples T over a regular category are characterized which have the property that every quotient object of a T-algebra cogenerates some quotient algebra: these are precisely the right exact triples, preserving colimits of quotient chains. This improves a result of Michael Barr (J. Pure Appl. Algebra 4 (1974), 1–8) that every right exact, finitary triple has the investigated property. This result is related to categorical automata, since a triple has the above property iff triple machines admit a minimal realization of every behavior.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 355 - 370
Copyright
Copyright © Australian Mathematical Society 1976

References

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