nLab acyclic object

Context

Homological algebra

homological algebra

Introduction

diagram chasing

Contents

Definition

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

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

Properties

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

Last revised on March 17, 2016 at 11:30:39. See the history of this page for a list of all contributions to it.