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Corings and comodules

✍ Scribed by Tomasz Brzezinski, Robert Wisbauer

Book ID
127421055
Publisher
Cambridge University Press
Year
2003
Tongue
English
Weight
2 MB
Series
London Mathematical Society lecture note series 309
Category
Library
City
Cambridge; New York
ISBN
0521539315

No coin nor oath required. For personal study only.

✦ Synopsis

After describing the module-theoretic aspects of coalgebras over commutative rings, this volume defines corings as coalgebras for non-commutative rings. Topics covered include module-theoretic aspects of corings (such as the relation of comodules to special subcategories of modules: sigma-type categories); connections between corings and extensions of rings; properties of new examples of corings associated to entwining structures; generalizations of bialgebras such as bialgebroids and weak bialgebras; and the appearance of corings in non-commutative geometry.

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We study the various categories of corings, coalgebras, and comodules from a categorical perspective. Emphasis is given to the question which properties of these categories can be seen as instances of general categorical resp. algebraic results. However, we also obtain new results concerning the exi