# 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 ${\displaystyle u:A\to M}$, for some M, such that ${\displaystyle F(u)=0}$. 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.