  Van den Bergh has defined the blowup of a noncommutative surface at a point
lying on a commutative divisor. We study one aspect of the construction, with
an eventual aim of defining more general kinds of noncommutative blowups. Our
basic object of study is a quasi-scheme X (a Grothendieck category). Given a
closed subcategory Z, in order to define a blowup of X along Z one first needs
to have a functor F which is an analog of tensoring with the defining ideal of
Z. Following Van den Bergh, a closed subcategory Z which has such a functor is
called well-closed. We show that well-closedness can be characterized by the
existence of certain projective effacements for each object of X, and that the
needed functor F has an explicit description in terms of such effacements. As
an application, we prove that closed points are well-closed in quite general
quasi-schemes.
