nLab
abelian subcategory

Definition

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

References

Section 1.2 of

• Charles Weibel, An Introduction to Homological Algebra