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

Erratum:
Proc. Amer. Math. Soc. **25** (1970), 922.

MathSciNet review:
0258712

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the category of commutative rings with unity and unity-preserving homomorphisms, and let be a small algebraic theory, i.e., an algebraic theory with a rank in the sense of Linton. The category of -coalgebras in is the category of coproduct-preserving functors . We prove that the standard forgetful functor has a right adjoint .

**[1]**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****[2]**I. G. Macdonald,*Algebraic geometry. Introduction to schemes*, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR**0238845**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1970-0258712-X

Keywords:
Algebraic theory with a rank,
right adjoint,
cosolution set,
tensor product of rings

Article copyright:
© Copyright 1970
American Mathematical Society