Formally smooth map

In differential geometry and related fields, a **formally smooth map** generally refers to a type of map that behaves smoothly at a certain level, even if it may not be globally smooth in the traditional sense across its entire domain. The concept is often discussed in the context of algebraic geometry and singularity theory. To provide a clearer understanding: 1. **Smooth Maps**: A smooth map is typically a function between differentiable manifolds that is infinitely differentiable.