Proceedings of the American Mathematical Society

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



Toposes, monoid actions, and universal coalgebra

Author: Robert C. Davis
Journal: Proc. Amer. Math. Soc. 98 (1986), 547-552
MSC: Primary 18B25; Secondary 18C15, 20M50
MathSciNet review: 861747
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Abstract: A category cotripleable over Sets may be a topos, or may fail to be a topos in at least two distinct ways. One class of examples involves the category of $ M$-sets and "strong" homomorphisms. For finite monoids $ M$, this category is cotripleable iff the left ideals of $ M$ are totally ordered by inclusion.

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Keywords: Cotripleable category, right adjoint, terminal object, elementary topos, subobject classifier, exponential object, monoid, left ideal, $ \mathcal{L}$-class
Article copyright: © Copyright 1986 American Mathematical Society