Yes of course. Pretty much all of algebraic geometry (the study of curves and surfaces defined by families of polynomial equations) owes its current life force

Yes of course. Pretty much all of algebraic geometry (the study of curves and surfaces defined by families of polynomial equations) owes its current life force to the sweeping reforms it undertook by utilizing category theory in the '50s and '60s. There are a number of conjectures (most notably, the Weil conjectures) whose proofs are attributed directly to the use of category theory.