Let $\mathcal{X}$ be an additive full subcategory of an abelian category. It is a classical fact that if $\mathcal{X}$ is contravariantly finite. then the category $\mathsf {mod}\. \mathcal{X}$ of finitely presented right $\mathcal{X}$-modules is abelian. https://jeepworldes.shop/product-category/hitches/
Resolving subcategories whose finitely presented module categories are abelian
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