Acyclic object - Alchetron, The Free Social Encyclopedia

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

F : C → D ,

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

R i F ( A ) = 0 for all i > 0 ,

where R i F are the right derived functors of F .

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