nLab
abelian subcategory

Definition

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

References

Section 1.2 of

• Charles Weibel, An Introduction to Homological Algebra