acyclic object

(also nonabelian homological algebra)

For $F : \mathcal{A} \to \mathcal{B}$ a left exact additive functor between abelian categories, an object $A \in \mathcal{A}$ is $F$-**acyclic** if the right derived functor of $F$ has no cohomology on $A$ in positive degree

$(p \gt 0) \Rightarrow R^p F A = 0
\,.$

A resolution by $F$-acyclic objects serves to compute the derived functor of $F$. See at *derived functor in homological algebra β Via acyclic resolutions*

Revised on March 17, 2016 11:30:39
by Urs Schreiber
(194.210.224.243)