??the relationship between homotopy limits and homotopy colimits of spectrums that we're imagining... that they're somehow almost the same thing in fair generality, and that preservation of one amounts to preservation of the other... ??or something like that??... trying to imagine this as some sort of more perfect form of the relationship between finite products and finite coproducts in an abelian-group-enriched category... (??is there any nice way to break up the progression towards the more perfect form into stages??) ...??compare to relationship between limits and colimits of truth values?? ??something??? (??level slip??...) ...??where preservation of one is very different from preservation of the other, despite some sort of close relationship... ??....