Lie Calculus

Abstract: We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher order theory naturally involves higher algebra (n-fold groupoids).(conceptual, topological) differential calculus, groupoids, higher algebra($n$-fold groupoids), Lie group, Lie groupoid, tangent groupoid, cubes of rings