Mon 26 May 2008
Kan Extensions III: As Ends and Coends
Posted by Edward Kmett under Category Theory , Haskell , Kan Extensions , Mathematics[9] Comments
Grant B. asked me to post the derivation for the right and left Kan extension formula used in previous Kan Extension posts (1,2). For that we can turn to the definition of Kan extensions in terms of ends, but first we need to take a couple of steps back to find a way to represent (co)ends in Haskell.

and
consists of a pair of functors
, and
and a natural isomorphism:
the left adjoint functor, and
the right adjoint functor and
an adjoint pair, and write this relationship as 