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Colimits of algebras revisited

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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It has “been open for some time whether, given an algebraic theory (triple, monad) Π in a cocomplete category K, also the category KΠ of Π-algebras must be cocomplete. We solve this in the negative by exhibiting a free algebraic theory Π in the category Gra of graphs such that GraΠ is not cocomplete. Further, we improve somewhat the well-known colimit theorem of Barr and Linton by showing that the base category need not be complete.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 3 , December 1977 , pp. 433 - 450
Copyright
Copyright © Australian Mathematical Society 1977

References

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