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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
DOI: https://doi.org/10.1090/S0002-9939-1986-0861747-9
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.


References [Enhancements On Off] (What's this?)

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  • [3] Robert C. Davis, Combinatorial examples in universal coalgebra, Proc. Amer. Math. Soc. 89 (1983), 32-34. MR 706504 (85i:18010a)
  • [4] -, Combinatorial examples in universal coalgebra. III, Proc. Amer. Math. Soc. 92 (1984), 332-334. MR 759647 (85i:18010c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0861747-9
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

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