Lemma 4.10.
Assuming that:
J
a
diagram
shape
D
has all
limits
of shape
J
G
:
D
→
C
preserves
all
limits
of shape
J
Then
for each
A
∈
ob
C
,
(
A
↓
G
)
has
limits
of shape
J
and the forgetful
functor
(
A
↓
G
)
→
U
D
creates them.