Colimits of algebras revisited
- 1 December 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 17 (3) , 433-450
- https://doi.org/10.1017/s0004972700010704
Abstract
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.Keywords
This publication has 5 references indexed in Scilit:
- Algebraic TheoriesPublished by Springer Nature ,1976
- Machines in a Category: An Expository IntroductionSIAM Review, 1974
- Categories for the Working MathematicianPublished by Springer Nature ,1971
- Coequalizers and free triplesMathematische Zeitschrift, 1970
- Coequalizers in categories of algebrasLecture Notes in Mathematics, 1969