# nLab acyclic object

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

### Theorems

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

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

Created on November 23, 2010 09:58:43 by Urs Schreiber (87.212.203.135)