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Proceedings of the American Mathematical Society

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

 
 

 

Free coalgebras in a category of rings


Author: Robert Davis
Journal: Proc. Amer. Math. Soc. 25 (1970), 155-158
MSC: Primary 08.30; Secondary 18.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0258712-X
Erratum: Proc. Amer. Math. Soc. 25 (1970), 922.
MathSciNet review: 0258712
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathcal {R}$ be the category of commutative rings with unity and unity-preserving homomorphisms, and let $\Pi$ be a small algebraic theory, i.e., an algebraic theory with a rank in the sense of Linton. The category $\mathcal {A}$ of $\Pi$-coalgebras in $\mathcal {R}$ is the category of coproduct-preserving functors ${\Pi ^{\ast }} \to \mathcal {R}$. We prove that the standard forgetful functor $U:\mathcal {A} \to \mathcal {R}$ has a right adjoint $V$.


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

  • F. E. J. Linton, Some aspects of equational categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 84–94. MR 0209335
  • I. G. Macdonald, Algebraic geometry. Introduction to schemes, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0238845

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Keywords: Algebraic theory with a rank, right adjoint, cosolution set, tensor product of rings
Article copyright: © Copyright 1970 American Mathematical Society