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 effaceable δ-functor (i.e., effaceable in each positive degree) is universal.

References

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

External links

• Meaning of “efface” in “effaceable functor” and “injective effacement”