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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Quasi-cotripleable categories

Author: Robert C. Davis
Journal: Proc. Amer. Math. Soc. 35 (1972), 43-48
MSC: Primary 18C15
MathSciNet review: 0316531
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Abstract: A category is quasi-cotripleable over the category of sets if it has all the properties of cotripleable categories except the right adjoint to the forgetful functor. Problems involving such categories are illustrated by categories of relational structures, and by categories of sets acted on by a monoid with open homomorphisms for maps. A characterization is given in terms of generalized operators and relations.

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Keywords: Cotripleable category, right adjoint, cosolution-set condition, quasi-cotripleable category, limit ordinal, universal sentence, positive sentence, admissible sentence, finite cyclic monoid, proper class, colimit, density cotriple
Article copyright: © Copyright 1972 American Mathematical Society