• Source: 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
→
M


{\displaystyle u:A\to M}

, for some M, such that



F
(
u
)
=
0


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




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External links


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

Kata Kunci Pencarian:

• Effaceable functor
• Delta-functor
• Alexander Grothendieck
• List of Latin verbs with English derivatives
• Séminaire Nicolas Bourbaki (1950–1959)