Acyclic object

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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 F, or simply an F-acyclic object, is an object A in such that

for all ,

where RⁱF are the right derived functors of F.

[edit] References

• S. Caenepeel, Brauer Groups, Hopf Algebras, and Galois Theory, Springer Verlag, 1998, ISBN 079234829X. P.454.