°Given
categories C and
D and
functors F and
G both going from
C to
D, then a transformation
η from
F to
G consists of components
ηX:
F(
X) →
G(
X), indexed by objects
X of
C, which are
morphisms in
D. The transformation is said to be natural if for any arrow
f:
X →
Y in
C, the following naturality condition is satisfied: .