PlanetPhysics/Hereditary Category

Let $$\mathcal{C}$$ be a locally small $$\mathcal{A}b3$$-category. A subcategory $$\mathcal{A}$$ of $$\mathcal{C}$$ is called hereditary if it verifies the following condition: if $$Y$$ is an object in a full subcategory $$\mathcal{F}$$ of $$\mathcal{C}$$, then any subobject of $$Y$$ is also in $$\mathcal{F}$$.