Kan Extension

A universal construction that produces the best approximation of a functor F along another functor K, yielding a left Kan extension Lan_K F (colimit-based) or a right Kan extension Ran_K F (limit-based) characterized by universal natural transformations.

A universal construction that extends a functor along another functor in the best possible way, producing left or right Kan extensions characterized by universal mapping properties that generalize limits, colimits and adjoints.