Generators for comonoids and universal constructions

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• 作者：Adnan H. Abdulwahid ; Miodrag C. Iovanov
• 关键词：Monoid ; Comonoid ; Free monoid ; Cofree ; Coalgebra ; Coring ; (Co)module coalgebra ; Complete ; Limits ; Bialgebra ; Hopf algebra
• 刊名：Archiv der Mathematik
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：106
• 期：1
• 页码：21-33
• 全文大小：515 KB
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• 作者单位：Adnan H. Abdulwahid (1)
  Miodrag C. Iovanov (1) (2)
  
  1. Department of Mathematics, University of Iowa, MacLean Hall, Iowa City, IA, USA
  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

We investigate cofree coalgebras, and limits and colimits of coalgebras in some abelian monoidal categories of interest, such as bimodules over a ring, and modules and comodules over a bialgebra or Hopf algebra. We find concrete generators for the categories of coalgebras in these monoidal categories, and explicitly construct cofree coalgebras, products and limits of coalgebras in each case. This answers an open question in Agore (Proc Am Math Soc 139:855–863, 2011) on the existence of a cofree coring, and constructs the cofree (co)module coalgebra on a B-(co)module, for a bialgebra B.