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Proceedings of the American Mathematical Society

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



Multivalued operations and universal coalgebra

Author: Robert C. Davis
Journal: Proc. Amer. Math. Soc. 32 (1972), 385-388
MSC: Primary 20M30; Secondary 08A25, 18C15
MathSciNet review: 0311826
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Abstract: We define a type of representation of a semigroup by relations on a set, more general than the representation by transformations, which leads to a category cotripleable over the category of sets. This result motivates a generalization to higherorder operations and a concept of cotheory resembling that of theory in universal algebra.

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  • [1] R. C. Davis, Abstract universal algebra, Dissertation, Tulane University, New Orleans, La., 1967.
  • [2] -, Quasicotripleable categories, Proc. Amer. Math. Soc. (to appear).
  • [3] J. Duskin, Variations on Beck’s tripleability criterion, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 74–129. MR 0252471
  • [4] 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
  • [5] Bodo Pareigis, Kategorien und Funktoren, Mathematische Leitfäden, B. G. Teubner, Stuttgart, 1969 (German). MR 0265427

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Keywords: Semigroup, representation, cotripleable category, right adjoint, colimit, right complete category, cosolution set, precise cotripleableness condition, tractable standard cotheory
Article copyright: © Copyright 1972 American Mathematical Society