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Limits of coalgebras, bialgebras and Hopf algebras


Author: A. L. Agore
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
Published electronically: August 18, 2010
MathSciNet review: 2745638
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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

DOI: https://doi.org/10.1090/S0002-9939-2010-10542-7
Keywords: Product of coalgebras, bialgebras, Hopf algebras
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.