Book contents
- Frontmatter
- Contents
- 0 Introduction
- I Algebras and modules
- II Quivers and algebras
- III Representations and modules
- IV Auslander–Reiten theory
- V Nakayama algebras and representation–finite group algebras
- VI Tilting theory
- VII Representation–finite hereditary algebras
- VIII Tilted algebras
- IX Directing modules and postprojective components
- A Appendix: Categories, functors, and homology
- Bibliography
- Index
- List of symbols
A - Appendix: Categories, functors, and homology
Published online by Cambridge University Press: 12 January 2010
- Frontmatter
- Contents
- 0 Introduction
- I Algebras and modules
- II Quivers and algebras
- III Representations and modules
- IV Auslander–Reiten theory
- V Nakayama algebras and representation–finite group algebras
- VI Tilting theory
- VII Representation–finite hereditary algebras
- VIII Tilted algebras
- IX Directing modules and postprojective components
- A Appendix: Categories, functors, and homology
- Bibliography
- Index
- List of symbols
Summary
For the convenience of the reader, we collect here the notations and terminology we use on categories, functors, and homology, and we recall some of the basic facts from category theory and homological algebra needed in the book.
We introduce the notions of category, additive category, K-category, abelian category, and the (Jacobson) radical of an additive category. We also collect basic facts from category theory and homological algebra. In this appendix we do not present proofs of the results, except for a few classical theorems that we frequently use in the book. For more details and complete proofs, the reader is referred to the following textbooks and papers on this subject, and.
- Type
- Chapter
- Information
- Elements of the Representation Theory of Associative AlgebrasTechniques of Representation Theory, pp. 404 - 436Publisher: Cambridge University PressPrint publication year: 2006