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

Schanuel's lemma

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.