# Equivalences between stable categories

Thanks to cnblog give me the access of uploading pdf.

This is a part of lecture notes of the course here. The most resource including is not easy to find in textbooks, so I think it will help if I posted in the internet.

## Preface

We should follow Zimmermannian book, but we decided to give up for some reason. In this note, we assume reader knows the basic of representation of associative algebra very well (e.g. what is quiver, why projective cover always exists, what is Morita equivalence, etc). We recommend the first 3 chapters of

- Ibrahim Assem, Daniel Simson, and Andrzej Skowronski. Elements of the Representation Theory of Associative Algebras. Volume 1 Techniques of Representation Theory.

for beginner. We also assume reader has a very good command of Homological algebra (e.g. what is Ext, what is long exact sequence, what is . ). I recommend the second chapter of

- Benson. D.J. Representation and cohomology.

for a quick introduction. I am not native speaker, so sorry for hundreds of grammar and spelling mistakes and abusage of words and punctuation. It is a hurry work, so there must be a lot of typos. Sorry for not detailed reference list.