nLab
cochain complex

Contents

Context

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Idea

A cochain complex V V^\bullet in an Ab-enriched category CC may be regarded as a chain complex (see there for more) in CC, but with the sign of the \mathbb{Z}-grading reversed.

This means that for a cochain complex (V ,d)(V^\bullet,d) the differential (or coboundary operator) dd increases the degree

d:V kV k+1. d \colon V^{k} \to V^{k+1} \,.

Examples

Last revised on July 10, 2021 at 12:19:22. See the history of this page for a list of all contributions to it.