Hermann, Reiner: Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology. 2013
Inhalt
- Abstract
- Zusammenfassung
- Acknowledgements
- Introduction
- Chapter 1. Prerequisites
- Chapter 2. Extension categories
- 2.1. Definition and properties
- 2.2. Homotopy groups
- 2.3. Lower homotopy groups of extension categories
- 2.4. n-Extension closed subcategories
- Chapter 3. The Retakh isomorphism
- 3.1. An explicit description
- 3.2. Compatibility results
- 3.3. Extension categories for monoidal categories
- Chapter 4. Hochschild cohomology
- Chapter 5. A bracket for monoidal categories
- 5.1. The Yoneda product
- 5.2. The bracket and its properties
- 5.3. The module case – Schwede's original construction
- 5.4. Morita equivalence
- 5.5. The monoidal category of bimodules
- Chapter 6. Application I: The kernel of the Gerstenhaber bracket
- 6.1. Introduction and motivation
- 6.2. Hopf algebroids
- 6.3. A monoidal functor
- 6.4. Specialization to Hopf algebras
- 6.5. Comparison to Linckelmann's result
- Chapter 7. Application II: The Ext-algebra of the identity functor
- 7.1. The evaluation functor
- 7.2. Exact endofunctors
- 7.3. Ext-algebras and adjoint functors
- 7.4. Hochschild cohomology for abelian categories
- Chapter 8. Open problems
- Appendix A. Basics
- A.1. Homological lemmas
- A.2. Algebras, coalgebras, bialgebras and Hopf algebras
- A.3. Examples: Hopf algebras
- Bibliography