Effaceable functor

In mathematics, an effaceable functor is an additive functor "F" between abelian categories "C" and "D" for which, for each object "A" in "C", there exists a monomorphism formula_1, for some "M", such that formula_2. Similarly, a coeffaceable functor is one for which, for each "A", there is an epimorphism into "A" that is killed by "F". The notions were introduced in Grothendieck's Tohoku paper.
A theorem of Grothendieck says that every effaceable δ-functor (i.e., effaceable in each degree) is universal.