Limits of Coalgebras, Bialgebras and Hopf Algebras
Quantum Algebra
2014-02-24 v2 Category Theory
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 explicit description for limits in the above categories is given.
Cite
@article{arxiv.1003.0318,
title = {Limits of Coalgebras, Bialgebras and Hopf Algebras},
author = {A. L. Agore},
journal= {arXiv preprint arXiv:1003.0318},
year = {2014}
}
Comments
Minor changes from previous version. To appear in Proceedings of the American Mathematical Society