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

Contents

Definition

In homological algebra:

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 \,.

Properties

A resolution by FF-acyclic objects serves to compute the derived functor of FF. See at derived functor in homological algebra – Via acyclic resolutions

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