# Lie Calculus

## TL;DR

Lie Calculus unifies differential calculus and Lie theory through the use of groupoids, extending to higher algebra with n-fold groupoids, providing a conceptual framework linking these mathematical areas.

## Contribution

It introduces Lie Calculus as a unified perspective connecting differential calculus and Lie theory via groupoids, including higher algebraic structures.

## Key findings

- Unified framework for differential calculus and Lie theory
- Use of groupoids as a conceptual link
- Extension to higher algebra with n-fold groupoids

## 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