# Commit 2020-08-28 05:18 513f7407

View on Github →feat(topology/sheaves): checking the sheaf condition under a forgetful functor (#3609)

# Checking the sheaf condition on the underlying presheaf of types.

If `G : C ⥤ D`

is a functor which reflects isomorphisms and preserves limits
(we assume all limits exist in both `C`

and `D`

),
then checking the sheaf condition for a presheaf `F : presheaf C X`

is equivalent to checking the sheaf condition for `F ⋙ G`

.
The important special case is when
`C`

is a concrete category with a forgetful functor
that preserves limits and reflects isomorphisms.
Then to check the sheaf condition it suffices
to check it on the underlying sheaf of types.