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