# Effaceable functor

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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 , for some *M*, such that . 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.