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

A theorem of Grothendieck says that every effaceble δ-functor (i.e., effaceable in each degree) is universal.

Further reading

• http://math.stackexchange.com/questions/44382/meaning-of-efface-in-effaceable-functor-and-injective-effacement

References

• Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157