Re Koszul duality
Mar. 14th, 2020 09:55 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
posicSo my feeling is that, as a general rule, there is as much Koszul duality as anybody is likely to ever need, provided that they are prepared to stomach the technical complexity of it (and people almost never are). If you want a substantial increase in generality without a related increase in complexity, that's a different question.
The problem is that people have to learn the basics of what Koszul duality is, in a context similar to what they want to have. Then they will see themselves how to adapt it to their situation, generalize etc. The observable situation is that, instead of learning the basics or working their way into understanding the subject, most people are asking me badly posed, confused questions. This is like someone who has not mastered tensors in linear algebra asking me if there exist tensors over curved surfaces. "Yes, they do exist" -- is the answer. But it is of little help to such a student.
The problem is that people have to learn the basics of what Koszul duality is, in a context similar to what they want to have. Then they will see themselves how to adapt it to their situation, generalize etc. The observable situation is that, instead of learning the basics or working their way into understanding the subject, most people are asking me badly posed, confused questions. This is like someone who has not mastered tensors in linear algebra asking me if there exist tensors over curved surfaces. "Yes, they do exist" -- is the answer. But it is of little help to such a student.
