nLab
acyclic object

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

For F:π’œβ†’β„¬F : \mathcal{A} \to \mathcal{B} a left exact additive functor between abelian categories, an object Aβˆˆπ’œA \in \mathcal{A} is FF-acyclic if the right derived functor of FF has no cohomology on AA in positive degree

(p>0)β‡’R pFA=0. (p \gt 0) \Rightarrow R^p F A = 0 \,.

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