toRan
and fromRan
witness an adjunction from Compose[G,_,_]
to Ran[G,_,_]
.
This is the natural transformation that defines a right Kan extension.
The universal property of a right Kan extension.
The universal property of a right Kan extension. The functor Ran[G,H,_]
and the
natural transformation gran[G,H,_]
are couniversal in the sense that for any
functor K
and a natural transformation s
from K[G[_]]
to H
, a unique
natural transformation toRan
exists from K
to Ran[G,H,_]
such that
for all k
, gran(toRan(k)) = s(k)
.