Timeline for Is the unbounded derived $\infty$-category of a general abelian category stable?

6 events

when toggle format	what		by	license	comment
Nov 19 at 17:01	comment	added	Z. M		Oh, what I had in my mind was incorrect. I thought of stable envelope of additive categories, but here, we need stable envelope of exact categories.
Nov 19 at 14:07	comment	added	Victor Saunier		@Z.M unless I misunderstand what you ask, the above-cited theorem precisely says the two agree.
Nov 19 at 12:26	comment	added	Z. M		I am confused. What is the relation between the bounded derived category of a small abelian category with its stable envelope.
Nov 19 at 8:32	comment	added	Victor Saunier		As David's answer below illustrates, the large derived bounded category is often constructed as a localisation, and this means one should probably be careful with the set-theory. For example, if your abelian category is locally presentable, then you should be able to reduce to the small case.
Nov 19 at 7:48	comment	added	Lin Chen		I agree. But in the classical theory, people also considered unbounded derived category of small abelian categories. For instance, arxiv.org/pdf/2003.11261.
Nov 18 at 12:26	history	answered	Victor Saunier	CC BY-SA 4.0