Kan extension

In category theory, a **Kan extension** is a construction used to generalize the idea of extending functions or functors across categories. More specifically, Kan extensions can be thought of as a way to extend a functor defined on a small category to a functor defined on a larger category, while maintaining certain properties related to limits or colimits. There are two types of Kan extensions: **left Kan extensions** and **right Kan extensions**.