Universal Differential Calculus

Universal Differential Calculus is a mathematical framework that generalizes traditional calculus to a wide variety of algebraic structures, such as non-commutative algebras, beyond standard functions. It provides a systematic way to define derivatives and differentials in settings where usual calculus notions don’t directly apply, using universal objects called differential calculi. This approach allows mathematicians to study "calculus-like" concepts in abstract contexts, which is essential in areas like non-commutative geometry and algebraic topology. Essentially, it creates a unifying language for differentiation that extends beyond classic calculus to more complex mathematical structures.