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Generators for comonoids and universal constructions
Journal article   Open access   Peer reviewed

Generators for comonoids and universal constructions

Adnan Abdulwahid and Miodrag Iovanov
Archiv der Mathematik, Vol.106(1), pp.21-33
01/2016
DOI: 10.1007/s00013-015-0826-6
url
https://arxiv.org/pdf/1603.00108View
Open Access

Abstract

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.
Mathematics Bialgebra 16S40 Complete Monoid Hopf algebra (Co)module coalgebra 18A35 Coalgebra Limits Comonoid Cofree Mathematics, general Free monoid 18A40 Coring 16T15

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