Quasi-cotripleable categories

Author:
Robert C. Davis

Journal:
Proc. Amer. Math. Soc. **35** (1972), 43-48

MSC:
Primary 18C15

DOI:
https://doi.org/10.1090/S0002-9939-1972-0316531-1

MathSciNet review:
0316531

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Abstract | References | Similar Articles | Additional Information

Abstract: A category is quasi-cotripleable over the category of sets if it has all the properties of cotripleable categories except the right adjoint to the forgetful functor. Problems involving such categories are illustrated by categories of relational structures, and by categories of sets acted on by a monoid with open homomorphisms for maps. A characterization is given in terms of generalized operators and relations.

**[1]**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups. Vol. I*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR**0132791****[2]**P. M. Cohn,*Universal algebra*, Harper & Row, Publishers, New York-London, 1965. MR**0175948****[3]**R. C. Davis,*Abstract universal algebra*, Dissertation, Tulane University, New Orleans, La., 1967.**[4]**Robert Davis,*Universal coalgebra and categories of transition systems*, Math. Systems Theory**4**(1970), 91–95. MR**0268243**, https://doi.org/10.1007/BF01705889**[5]**John R. Isbell,*A note on complete closure algebras*, Math. Systems Theory**3**(1969), 310–312. MR**0252296**, https://doi.org/10.1007/BF01691060**[6]**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****[7]**F. E. J. Linton,*An outline of functorial semantics*, Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, Berlin, 1969, pp. 7–52. MR**0244340**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0316531-1

Keywords:
Cotripleable category,
right adjoint,
cosolution-set condition,
quasi-cotripleable category,
limit ordinal,
universal sentence,
positive sentence,
admissible sentence,
finite cyclic monoid,
proper class,
colimit,
density cotriple

Article copyright:
© Copyright 1972
American Mathematical Society