1
vote
1answer
294 views

Why does Neeman avoid t-structures?

I have a simple question: the book "Triangulated Categories" by A. Neeman aims to be an exhaustive reference about the whole (basic) theory of triangulated categories. So why there is only a single ...
1
vote
1answer
75 views

On two notions of 'generators' for a 'large' triangulated category

Let $C$ be a triangulated category that is closed with respect to arbitrary small coproducts; let $D$ be some class of objects of $C$. Then it would be natural to say that $D$ generates $C$ either if ...
3
votes
1answer
184 views

Bousfield localization before and after taking homotopy

The ncatlab says: Under suitable conditions it should be true that for $C$ a model category whose homotopy category $\mathrm{Ho}(C)$ is a triangulated category the homotopy category of a left ...
10
votes
0answers
364 views

The derived category of integral representations of a Dynkin quiver.

Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $Q$. Let's write ...
19
votes
0answers
666 views

Pre-triangulated category that isn't triangulated

I've been working through some of the early parts of Neeman's book on triangulated categories, and he mentions that he does not know of a pre-triangulated category that is not triangulated. Is this ...