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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Limits of coalgebras, bialgebras and Hopf algebras
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by A. L. Agore PDF
Proc. Amer. Math. Soc. 139 (2011), 855-863 Request permission

Abstract:

We give the explicit construction of the product of an arbitrary family of coalgebras, bialgebras and Hopf algebras: it turns out that the product of an arbitrary family of coalgebras (resp. bialgebras, Hopf algebras) is the sum of a family of coalgebras (resp. bialgebras, Hopf algebras). The equalizers of two morphisms of coalgebras (resp. bialgebras, Hopf algebras) are also described explicitly. As a consequence the categories of coalgebras, bialgebras and Hopf algebras are shown to be complete, and a complete description for limits in the above categories is given.
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Additional Information
  • A. L. Agore
  • Affiliation: Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, RO-010014 Bucharest 1, Romania – and – Department of Mathematics, Academy of Economic Studies, Piata Romana 6, RO-010374 Bucharest 1, Romania
  • Email: ana.agore@fmi.unibuc.ro
  • Received by editor(s): September 16, 2009
  • Received by editor(s) in revised form: April 14, 2010
  • Published electronically: August 18, 2010
  • Additional Notes: The author acknowledges partial support from CNCSIS grant 24/28.09.07 of PN II “Groups, quantum groups, corings and representation theory”.

    • Dedicated: Dedicated to the memory of Professor S. Ianuş
  • Communicated by: Martin Lorenz
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 855-863
  • MSC (2000): Primary 16W30, 18A30, 18A40
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10542-7
  • MathSciNet review: 2745638