Given a stable quasicategory $C$, what are the conditions required of a subcategory for it to descend to a localizing subcategory in $Ho(C)$? Is it enough for it to be reflective? Perhaps exact and ...
I've been looking at various general strategies for proving that some category is triangulated, and Lurie manages to prove that a huge class of interesting examples of categories that we know about ...
Do you know natural examples of triangulated categories (or [presentable] stable $\infty$-categories) which are not compactly generated? (ideally they'd be defined algebraically, but curious to hear ...