Acyclic object explained

F : l{C}\to l{D} ,

an acyclic object with respect to

F , or simply an F -acyclic object, is an object A in l{C} such that{\rm R} ^{i} F (A) = 0 for all i> 0 ,

where

{\rm R} ^{i} F are the right derived functors of F .^[1]

Notes and References

1. Book: Caenepeel, Stefaan . Brauer groups, Hopf algebras and Galois theory . 0898.16001 . Monographs in Mathematics . 4 . Dordrecht . Kluwer Academic Publishers . 1998 . 1-4020-0346-3 . 454 .