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We give an overview of the recent approach to the integration of rough pathsthat reduces the problem to classical Young integration. As an application, weextend an argument of Schwartz to rough differential equations, and prove theexistence, uniqueness and continuity of the solution, which is applicable whenthe driving path takes values in nilpotent Lie group or Butcher group.

The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations