For an ideal

of a preadditive category

, we study when the canonical functor

is local. We prove that there exists a largest full subcategory

of

, for which the canonical functor

is local. Under this condition, the functor

, turns out to be a weak equivalence between

, and

. If

is additive (with splitting idempotents), then

is additive (with splitting idempotents). The category

is ample in several cases, such as the case when