For a closed subgroup
H
H
of a locally compact group
G
G
, it is shown that a covariant system
(
G
,
A
)
(G,A)
is induced from a covariant system
(
H
,
D
)
(H,D)
if (and only if) there exists a continuous
G
G
-equivariant map
φ
:
Pr
im
A
→
G
/
H
\varphi :\Pr {\text {im}}A \to G/H
.