somewhere recently i saw mention of something like "cohomological functors" in the context of triangulated categories, or something like that... probably wpa on "triangulated category"... ??might these have something to do with "bimodules between abelian (infinity,1)-categories" or something?? ... something about (infinity,1)-functors with one adjoint and thus (??) also the other... ??in certain "stable" context ... ???.....

??hmm, is the apparent fact that verdier invented triangulated categories perhaps a good sign in terms of trying to relate "verdier duality" to a sort of "equivalence" between homotopy limits and homotopy colimits in "the stable case" ( =?= the case of an "abelian (infinity,1)-category", or something like that) ?? ....