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

,

an acyclic object with respect to , or simply an -acyclic object, is an object in such that

for all ,

where are the right derived functors of .[1]

References

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  1. ^ Caenepeel, Stefaan (1998). Brauer groups, Hopf algebras and Galois theory. Monographs in Mathematics. Vol. 4. Dordrecht: Kluwer Academic Publishers. p. 454. ISBN 1-4020-0346-3. Zbl 0898.16001.