Natural Transformations

A natural transformation is a way to smoothly connect two different ways of converting one mathematical structure into another, ensuring this connection respects their inherent relationships. Think of it as a consistent, coherent set of mappings that translate the outputs of one process into the outputs of another, across all inputs, in a way that aligns perfectly with their original structures. It's like finding a perfectly tailored bridge that links two different but related pathways, maintaining harmony and structure throughout the transformation.