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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.

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

  • [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
    Bodo Pareigis, Categories and functors, Translated from the German. Pure and Applied Mathematics, Vol. 39, Academic Press, New York-London, 1970. MR 0265428

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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