**Contemporary Mathematics**

Volume: 431;
2007;
467 pp;
Softcover

MSC: Primary 18; 55; 81; 19;

**Print ISBN: 978-0-8218-3970-6
Product Code: CONM/431**

List Price: $141.00

AMS Member Price: $112.80

MAA Member Price: $126.90

**Electronic ISBN: 978-0-8218-8110-1
Product Code: CONM/431.E**

List Price: $133.00

AMS Member Price: $106.40

MAA Member Price: $119.70

# Categories in Algebra, Geometry and Mathematical Physics

Share this page *Edited by *
*Alexei Davydov; Michael Batanin; Michael Johnson; Stephen Lack; Amnon Neeman*

Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.

#### Readership

Graduate students and research mathematicians interested in category theory and its applications.

# Table of Contents

## Categories in Algebra, Geometry and Mathematical Physics

- Contents v6 free
- The beginnings of category theory in Australia 114 free
- Higher gauge theory 720
- Resolution of coloured operads and rectification of homotopy algebras 3144
- Simplicial monoids and Segal categories 5972
- Split extension classifier and centrality 8598
- Moore normalization and Dold-Kan theorem for semi-abelian categories 105118
- An intrinsic characterization of branched coverings 125138
- The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories 143156
- Abstract cellularization as a cellularization with respect to a set of objects 165178
- Batanin higher groupoids and homotopy types 171184
- Centres of monoidal categories of functors 187200
- Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions 203216
- Topological and conformal field theory as Frobenius algebras 225238
- Characterization of torsion theories in general categories 249262
- Weak units and homotopy 3-types 257270
- Quasi-categories vs Segal spaces 277290
- Introduction 277290
- 1. The model structure for quasi-categories 279292
- 2. The vertical and horizontal Reedy model structures 284297
- 3. Segal spaces 291304
- 4. Two equivalences with complete Segal spaces 297310
- 5. Two equivalences with Segal categories 303316
- 6. Addendum 308321
- 7. Appendix 308321
- 8. Epilogue 323336
- References 324337

- Parking functions and triangulation of the associahedron 327340
- La K-théorie d'un dérivateur triangulé 341354
- Appendice: Le Dérivateur Triangulé Associé à une Catégorie Exacte 369382
- Formal homotopy quantum field theories, II: simplicial formal maps 375388
- Three dimensional monad theory 405418
- Orientals 427440
- Weak complicial sets II: nerves of complicial Gray-categories 441454