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Galois Theory, Hopf Algebras, and Semiabelian Categories
Edited by: George Janelidze, Razmadze Mathematical Institute of the Georgian Academy of Sciences, Tbilisi, Republic of Georgia, Bodo Pareigis, University of Munich, Germany, and Walter Tholen, York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2004; 570 pp; hardcover
Volume: 43
ISBN-10: 0-8218-3290-5
ISBN-13: 978-0-8218-3290-5
List Price: US$150
Member Price: US$120
Order Code: FIC/43
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See also:

Monoidal Functors, Species and Hopf Algebras - Marcelo Aguiar and Swapneel Mahajan

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 up-to-date 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 higher-dimensional 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


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 semi-abelian 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 local-to-global 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 2-groupoids and low-dimensional cohomology of crossed modules
  • M. Gran -- Applications of categorical Galois theory in universal algebra
  • C. Hermida -- Fibrations for abstract multicategories
  • J. Huebschmann -- Lie-Rinehart 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. Martins-Ferreira -- Weak categories in additive 2-categories with kernels
  • T. Palm -- Dendrotopic sets
  • A. H. Roque -- On factorization systems and admissible Galois structures
  • P. Schauenburg -- Hopf-Galois and bi-Galois extensions
  • J. D. H. Smith -- Extension theory in Mal'tsev varieties
  • L. Sousa -- On projective generators relative to coreflective classes
  • J. J. Xarez -- The monotone-light 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
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