I think I found two core responsibilities of management at Adobe:
(1) You always stay on top of things and try to push them forward to the best of your ability.
(2) You build your company assets with care. Company assets for software are really the people that work here. That explicitly means you develop people in whatever capacity they do best.
That's for daily team leadership. There’s more around vision and risk taking, though I’ve not yet been able to distill that into a single sentence.