Commit 2020-08-28 05:18 513f7407View on Github →
feat(topology/sheaves): checking the sheaf condition under a forgetful functor (#3609)
Checking the sheaf condition on the underlying presheaf of types.
G : C ⥤ D is a functor which reflects isomorphisms and preserves limits
(we assume all limits exist in both
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.