Fields Institute Communications 2004; 570 pp; hardcover Volume: 43 ISBN10: 0821832905 ISBN13: 9780821832905 List Price: US$142 Member Price: US$113.60 Order Code: FIC/43
 This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an uptodate account of the many current connections among Galois theories, Hopf algebras, and semiabelian categories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higherdimensional structures. Articles are suitable for graduate students and researchers, specifically those interested in Galois theory and Hopf algebras and their categorical unification. Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in category theory and its use in Galois theory and Hopf algebras. Table of Contents  M. Barr  Algebraic cohomology: The early days
 F. Borceux  A survey of semiabelian categories
 D. Bourn  Commutator theory in regular Mal'cev categories
 D. Bourn and M. Gran  Categorical aspects of modularity
 R. Brown  Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional localtoglobal problems
 M. Bunge  Galois groupoids and covering morphisms in topos theory
 S. Caenepeel  Galois corings from the descent theory point of view
 B. Day and R. Street  Quantum categories, star autonomy, and quantum groupoids
 J. W. Duskin, R. W. Kieboom, and E. M. Vitale  Morphisms of 2groupoids and lowdimensional cohomology of crossed modules
 M. Gran  Applications of categorical Galois theory in universal algebra
 C. Hermida  Fibrations for abstract multicategories
 J. Huebschmann  LieRinehart algebras, descent, and quantization
 P. Johnstone  A note on the semiabelian variety of Heyting semilattices
 G. M. Kelly and S. Lack  Monoidal functors generated by adjunctions, with applications to transport of structure
 M. Khalkhali and B. Rangipour  On the cyclic homology of Hopf crossed products
 G. Lukács  On sequentially \(h\)complete groups
 J. L. MacDonald  Embeddings of algebras
 A. R. Magid  Universal covers and category theory in polynomial and differential Galois theory
 N. MartinsFerreira  Weak categories in additive 2categories with kernels
 T. Palm  Dendrotopic sets
 A. H. Roque  On factorization systems and admissible Galois structures
 P. Schauenburg  HopfGalois and biGalois extensions
 J. D. H. Smith  Extension theory in Mal'tsev varieties
 L. Sousa  On projective generators relative to coreflective classes
 J. J. Xarez  The monotonelight factorization for categories via preorders
 J. J. Xarez  Separable morphisms of categories via preordered sets
 S. Yamagami  Frobenius algebras in tensor categories and bimodule extensions
