**Fields Institute Communications**

Volume: 43;
2004;
570 pp;
Hardcover

MSC: Primary 08; 12; 13; 14; 16; 17; 18; 19; 22;

Print ISBN: 978-0-8218-3290-5

Product Code: FIC/43

List Price: $150.00

Individual Member Price: $120.00

**Electronic ISBN: 978-1-4704-3077-1
Product Code: FIC/43.E**

List Price: $150.00

Individual Member Price: $120.00

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# Galois Theory, Hopf Algebras, and Semiabelian Categories

Share this page *Edited by *
*George Janelidze; Bodo Pareigis; Walter Tholen*

A co-publication of the AMS and Fields Institute

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).

#### Table of Contents

# Table of Contents

## Galois Theory, Hopf Algebras, and Semiabelian Categories

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Algebraic cohomology: The early days 112
- A survey of semi-abelian categories 2738
- Commutator theory in regular Mal’cev categories 6172
- Categorical aspects of modularity 7788
- Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems 101112
- Galois groupoids and covering morphisms in topos theory 131142
- Galois corings from the descent theory point of view 163174
- Quantum categories, star autonomy, and quantum groupoids 187198
- Morphisms of 2-groupoids and low-dimensional cohomology of crossed modules 227238
- Applications of categorical Galois theory in universal algebra 243254
- Fibrations for abstract multicategories 281292
- Lie-Rinehart algebras, descent, and quantization 295306
- A note on the semiabelian variety of Heyting semilattices 317328
- Monoidal functors generated by adjunctions, with applications to transport of structure 319330
- On the cyclic homology of Hopf crossed products 341352
- On sequentially ℎ-complete groups 353364
- Embeddings of algebras 359370
- Universal covers and category theory in polynomial and differential Galois theory 373384
- Weak categories in additive 2-categories with kernels 387398
- Dendrotopic sets 411422
- On factorization systems and admissible Galois structures 463474
- Hopf-Galois and bi-Galois extensions 469480
- Extension theory in Mal’tsev varieties 517528
- On projective generators relative to coreflective classes 523534
- The monotone-light factorization for categories via preorders 533544
- Separable morphisms of categories via preordered sets 543554
- Frobenius algebras in tensor categories and bimodule extensions 551562
- Back Cover Back Cover1582

#### Readership

Graduate students and research mathematicians interested in category theory and its use in Galois theory and Hopf algebras.