Document Type

Dissertation

Date of Degree

Summer 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Miodrag C. Iovanov

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 nd 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 [4] on the existence of a cofree coring, and constructs the cofree (co)module coalgebra on a B-(co)module, for a bialgebra B.

Keywords

Associative Algebras, Category Theory, Comodules, Corings, Hopf Algebras

Pages

vi, 112 pages

Bibliography

Includes bibliographical references (pages 105-112).

Copyright

Copyright 2016 Adnan Hashim Abdulwahid

Included in

Mathematics Commons

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