Good morphisms of distinguished triangles: can Neeman's method be applied to the motivic stable homotopy category?
It is well known that non-uniqueness of a cone for a morphism in a triangulated category $C$ makes constructing exact functors (of triangulated categories) a difficult task. In section 3 of his "Some ...
On 'graded polarizable' triangulated categories; are there any mixed Galois module analogues known? Also on mixed realizations
There is a construction by Beilinson (in section 3 of "Notes on absolute Hodge cohomology") of the derived category of graded polarizable mixed Hodge complexes; he also proved that this category is ...
I'm curious to find out where the viewpoint of higher categories may be useful so here is a somewhat vague question (which may or may not have a reasonable answer). Given a triangulated category, one ...