Acyclic object

In mathematics, in the field of homological algebra, given an abelian category ${𝒞}$ having enough injectives and an additive (covariant) functor

$F:{𝒞}\to {𝒟}$,

an acyclic object with respect to $F$, or simply an $F$-acyclic object, is an object $A$ in ${𝒞}$ such that

${\mathrm{R}}^{i}F(A)=0$ for all $i>0$,

where ${\mathrm{R}}^{i}F$ are the right derived functors of $F$.

References

• Caenepeel, Stefaan (1998). Brauer groups, Hopf algebras and Galois theory. Monographs in Mathematics. 4. Dordrecht: Kluwer Academic Publishers. p. 454. ISBN 1-4020-0346-3.