# Commit 2022-04-03 11:32 12128187

View on Github →feat(category_theory/abelian): transferring "abelian-ness" across a functor (#13059)
If `C`

is an additive category, `D`

is an abelian category,
we have `F : C ⥤ D`

`G : D ⥤ C`

(both preserving zero morphisms),
`G`

is left exact (that is, preserves finite limits),
and further we have `adj : G ⊣ F`

and `i : F ⋙ G ≅ 𝟭 C`

,
then `C`

is also abelian.
See https://stacks.math.columbia.edu/tag/03A3