Acyclic object

In mathematics, in the field of homological algebra, given an abelian category 
formula_1 having enough injectives and an additive (covariant) functor 
an acyclic object with respect to formula_3, or simply an formula_3-acyclic object, is an object formula_5 in formula_1 such that
where formula_9 are the right derived functors of 
formula_3.