Higher topos and derived algebraic geometry are relatively new areas and probably fewer people are working on them compared to the majority of topologists or geometers. I believe higher categories should have great power in producing new results in algebra (K-theory, algebraic topology, algebraic geometry). What are some important applications of higher categories in these areas?
The use of higher categories seems to be closer to the nature of homotopy theory and algebraic K-theory. I have heard from people in algebraic K-theory that higher categories are very useful and can produce important new results. My feeling is that applications of higher categories in AG are less substantial as most algebraic geometers don't need many abstract settings. I will appreciate suggestions for references or overviews of applications in higher categories in K-theory, algebraic topology, algebraic geometry or homotopy theory.