Kan Extensions

Kan extensions are a mathematical concept used to extend or approximate functions between different categories while preserving their structure. Imagine having a way to translate or extend a process or relationship defined on a small system to a larger, more complex one, ensuring consistency. They serve as a universal tool for deriving the most natural or best possible extension of a structure from a part to a whole. In essence, Kan extensions provide a way to systematically generalize or extend functions, maintaining their core relationships and properties across different contexts within category theory.