nLab abelian subcategory

Contents

Context

Notions of subcategory

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

Definition

For 𝒜\mathcal{A} an abelian category an abelian subcategory is a subcategory 𝒜\mathcal{B} \to \mathcal{A} such that B\mathbf{B} is also abelian and such that every exact sequence in \mathcal{B} is also exact in 𝒜\mathcal{A}.

References

Section 1.2 of

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