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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information

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