If G
is left adjoint to F
, there is a natural isomorphism between
Lan[G,H,_]
and H[F[_]]
The universal property of a left Kan extension.
The universal property of a left Kan extension. The functor Lan[G,H,_]
and the
natural transformation glan[G,H,_]
are universal in the sense that for any
functor F
and a natural transformation s
from H
to F[G[_]]
, a unique
natural transformation toLan
exists from Lan[G,H,_]
to F
such that
for all h
, glan(h).toLan = s(h)
.
The left Kan extension of
H
alongG