For questions about left, right and absolute Kan extensions from category theory. Use in conjunction with the tag (category-theory).
Kan extensions are another fundamental universal construction in category theory which is closely related to (co)limits, (co)ends and also adjunctions. The slogan "All Concepts are Kan Extensions" explains its ultimate generality in category theory. The idea is to generalize the "notion of extending a function defined on a subset to a function defined on the whole set" into categories and functors. As it sounds possible extensions are not unique and not always exists due to obstructions of various forms. But sometimes there exists one or two "best" approximate extensions called left Kan extension and right Kan extension equip with similar but different universal properties.